A wizard in the party is using scorching ray in a forest. I'm just making up chances for a fire starting with missed attacks, which works fine for me, but wondering if are there any rules or anyone have any handy tables for fire and the ignition of combustibles? Do certain spells burn more hotly than others?

Nothing RAW that I'm aware of, but I've always believed it was difficult to start unintentional fires with magic due to casting times, durations, concentration, etc... although I confess concessions are always made for wild magic :)

Fire Bolt and Create Bonfire specify that they can catch items on fire. Scorching Ray doesn’t and in 5e if something isn’t in the rules then it doesn’t happen. So the wizard isn’t risking starting a forest fire because of how the spell works. 

DMs can always bend, add, or remove rules. If the forest has particularly dry leaves or brush, make sure you include that in descriptions, and a random chance to start fires when using fire damage (and maybe lightning) attacks is reasonable. A fire is not likely to start in a green forest though.

Quote from Tim >>

Fire Bolt and Create Bonfire specify that they can catch items on fire. Scorching Ray doesn’t and in 5e if something isn’t in the rules then it doesn’t happen. So the wizard isn’t risking starting a forest fire because of how the spell works. 

Stating that if it isn't in the rules that you can do it you there for cannot is too extreme in my view.  There are an awful lot of things that do not have rules that characters are routinely allowed to do.  For example there are no rules for using a torch to set something on fire.  By RAW a torch can't light a fire, because nothing in RAW says you can light a fire with a tinderbox "and in 5e if something isn't in the rules then it doesn't happen." Is anyone seriously going to argue that a torch can't be used to light a fire just because RAW doesn't say you can?

Scorching Ray says you create three rays of fire. Are you going to tell me with a straight face that fire in 5e can't set other things on fire? Because we already established that torches don't.  I say Scorching Ray can start fires.

Quote from DavetheLost >>

Are you going to tell me with a straight face that fire in 5e can't set other things on fire? Because we already established that torches don't. 

But DavetheLost....I can't set the clothing that you're wearing on fire with those amazing fire spells. D&D says that when items are worn or carried they are, by some strange magical means, fireproof! So....of course you can safely cast a spell that creates 3 rays of fire safely in a sawdust factory. About that whole torch thing, just, um, yea, it's D&D magic.

It's how the rules are written and it's part of how I pick the spells.  D&D's magic rules are what they are.

I hope you caught the sarcasm dripping off my post.

As to your decisions, they're valid and they're probably the better choices by RAW. However, I feel we are limited to a mechanical constraint in a game run mostly on imagination.

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Imagine if you will:

Your party walks around the corner, exiting the tower on to the ramparts. You see an Flesh Golem hurl a large wooden barrel down, below you see the fires of your liege's army burst as the oil in the barrel ignites as it smashes into the ground. You watch as the tents and materials within ignite. You know that this is going to make the siege take much longer as you're pretty certain that the weapons inside are going to be destroyed. Your friend, Jorim the Wizard, get's a crazy idea and charges at the Flesh Golem as it picks up another barrel. His fingers fanning out as his thumbs meet, you've seen this before, he casts Burning Hands. The wooden barrel drops to the ground unharmed, the Golem reels in pain and Jorim is shoved by the Golem falling 40 feet to the ground off the ramparts. 

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The underlined part is the bit I have issue with. Just because the barrel was being carried it is untouched, as per RAW. It doesn't matter that it was filled with oil, that it's made of wood, and that the spell cast was fire. Now, the thing about this is it punishes intelligent and tactical thinking.

You know, in real life a wooden barrel hit by a flamethrower would ignite, but this is D&D, you want to save that wooden barrel from burning, pick it up. Sure you'll burn, but that barrel is perfectly fine, and so is your clothing, so just your hands and face are burnt, the rest of you is fine. I am all for suspension of disbelief but that addendum to fire spells is immersion breaking at best. 

Fire Bolt might be able to set the barrel on fire because it can target objects

Interestingly I just came across this in the DMG, it is more of an example than a rule per se, but...

"Huge and Gargantuan Objects
Normal weapons are of little use against many Huge and Gargantuan objects, such as a colossal statue, towering column of stone, or massive boulder. That said, one torch can burn a Huge tapestry..."

D&D magic has some oddities to be sure. Like worn and carried objects not being affected by spells, except when they are.  Fireball doesn't set your clothes on fire, but Invisibility makes them invisible along with the rest of you. Another one that gets me is that Magic Missile can only target "creatures", so you can't hit a lantern with a Magic Missile to spill burning oil all over the place. It's a glowing dart of magical force, but it can't target non-creatures. Although Miriam-Webster gives an out for the hair-splitting rules lawyer the first definition it gives for creature is "something created either animate or inanimate". A lantern is something created...

Fire Bolt could target the barrel, but as long as it is being carried it won't ignite. Same "if it isn't being worn or carried".

Fire Storm lets you decide if you want to burn the plants or not, over wise flammable objects that are not being worn or carried ignite.

So I could carry an open can of gasoline through a Fire Storm spell, while being hit by a Fire Ball, with a mage targeting the gas with a Fire Bolt and it still wouldn't ignite!

I think this is a case where I liked 1e better. Items had to make a saving throw against fire, especially magical fire. So a Fire Ball might boil your potions, although being magic items they had a decent save.  I get that the addendum to the fire spells makes things simpler, but it strains credulity.

Target the barrel, the barrel begins to leak because of the damage. Then target the falling drops, they are no longer being worn or carried. The ignited drop falls on the golem and ignite other falling drops and the barrel. 

That would work. You could also target the pool of oil on the floor from the leaking barrel.

Most items that are particularly vulnerable to fire would say what happens when they are exposed to fire, thus negating the need to target the item in some convoluted way.

Similarly, a DM could dictate that the environment is such that any fire damage attacks that miss their target or has an aoe has a chance to start a forest fire.

The rules just try to keep things fair and simple, it is up to the DM to make things believable (and still fair).

The need for convoluted targeting is brought on by the specific rules of the spells in question. Worn or carried items are specifically not set on fire by those spells.  We are having a bit of fun with the situation that this creates.

A flaming arrow into the keg of oil would light it up just fine. It is not a general rule that worn or carried items cannot be set on fire. It is a specific rule for certain spells. Those spells will ignite other flammable items just fine.

We get that it creates a silly situation.

OH! I found another way to do it!

Flametongue: It says that it's on fire, says that it does fire damage, but does not have the addendum that worn/carried items aren't set on fire. Just run up and swing, huge boom! I'd suggest a Resist Elements spell or being closely related to something like a Red dragon before doing this though. Strange that a magical flaming weapon is more potent than the magic that created it :)

A Good DM would roll with the environmental hazard.  A bad DM is a slave to RAW.

Personally, I'd rule it something like this:
For magical fire (such as that created by spells), it normally doesn't set stuff on fire unless, for example, the spell description says it does. Non-magical fire, however, does light most stuff on fire, given the DM has enough grounds for whatever it may be to be able to catch on fire. Of course this could be worked around with creative thinking, such as if a player tried to use Flametongue (which would be magical fire) to light e.g. a pool of grease on fire.
As for the non-flammable worn and carried objects thing, I'd look at why that is the case. Of course a player wizard doesn't want to get hit by Burning Hands spell just to have their spellbook going up in flames, or going naked just because they didn't wear a fireproof robe that day. But when it comes to trying to fireproof an object just by picking it up, then you better have a good reason as to how that would work aside from just working through sheer RAW.

Of course this is just how I see it, and other people may disagree, in which case go ahead. I'm not one to change how you decide how to run the game. Just thought I'd add my own input to the discussion.

if you really want to do this this then here is my suggestion: 

on a critical failure make him roll percentage die. lets say anything over 50 lights the brush on fire.

on a regular miss the roll the percentage die. if its over say 75 it sets it on fire. 

the best part of dnd is fun is the point of it followed by story telling. if you as the DM think it would be fun for a wizard to accidentally burn down a forest then a wizard that sucks at spell casting can burn down a forest. but also maybe when the wizard sets fire to a forest a plot point in the story is the forest creatures attack him on site.

as far as fireproofing maybe a wizard specifically wears fire proofed clothes and protects his spell book. but maybe your plate wearing takes fire damage maybe d4 turns for effectively being in an oven. and maybe that same plate wearer takes an extra dmg die of lightning dmg for being in a conductor. youre the dm make it fun and exciting. these rules might make your players be a little more wise with their decisions too.

It takes a rather longish period of dry, hot weather for a forest to be any sort of flammable. Of course, when it is sufficiently dry, casting fire spells in one is a catastrophically bad idea. 

Now, a bog. See, bogs dry out much faster, and the bloody things just won't stop burning. As a kid, we built a fort. We were kids. We considered it the height of wisdom to make a carpet of dry grass - then light a small fire in an old paint can. Then someone (no no - certainly not me) accidentally kicked over the can, lit the carpet on fire, which in turn lit the very dry bog on fire. 

That burned for a week. We didn't earn a lot of praise for that.

Of course forest fires can last for longer, but this was an area of maybe one square mile - that burned and kept burning for a week. I don't know a lot about forest fires, we don't tend to get them here, but the fire fighters told me that bog fires are the worst. 

Would it be more correct to call it a peat fire?