If I cast catapult spell on my dagger what would you choose as the damage ? First time doing a sorcerer

Bludgeoning, as it says in the spell. If you really want to have some fun, try using catapult with flasks of oil, alchemist's fire, and caltrops or ball bearings. Your DM might switch the damage up to something else, like piercing with caltrops, but that would be a houserule.

Can you use it with the Magic Stone spell? Would that add more damage?

The simple answer is that RAW the Catapult spell does the damage Catapult says it does and nothing else - no matter what.

But if the DM feels that extra damage would be applicable with situations such as catapulting a big vial of acid that smashed as a result of the spell or something like that - then that's up to them.

I second what Emmber said. No matter what you affect with Catapult, it does 3d8 bludgeoning RAW. However, if you were to cast Catapult on, say, a Molotov cocktail, and if I were your DM, you bet your biscuits that I'd let some extra damage sneak its way in there.

But if you did catapult on holy water, alchemists fire or a type of acid in a glass bottle, it would break on impact and deal the extra damage from that.

So magic stones wouldn’t work but magic stones in a jar would?

RAW only the target and the object thrown take the 3d8 damage. If you're throwing a vial of acid it makes sense for the acid to splash the target if the vial breaks. But a jar with a magic stone in it - I don't really see the magic stone being able to hit the target just because the jar it was in broke.

So with some money spent a level 2 spell becomes more than the damage-dealing equivalent of a spell pumped up past level 20. *headshake*
4d8 from spell + 9 vials of Acid  (2d6= 18d6) = around 80 damage on average?
Sure, let them players do it. But immediately let them know not to be surprised if this suddenly becomes a favored tactic of enemies.

Allowing a player to throw a vial of acid with catapult and apply both the effect of the spell (4d8) and the vial of acid (2d6) is not the same thing as consenting to them filling one jar with multiple vials of acid and applying the damage dice of each acid dose separately (18d6). Rewarding creative thinking and use of resources is not the same thing as rewarding metagaming and exploitation. And if the DM feels that an in-game justification is needed for capping the effect, then there's no guarantee that the target is getting splashed by more acid just because more acid was thrown, most of those other 8 vials may just have splashed down on the ground around them. 

I'd be extremely likely to reward a crew that, say, catapults a small barrel of black powder (which smashes, and goes poof) and then another PC has a fire-igniting cantrip ready...

I love catapult as a spell. Since you don't have to touch the object that you are catapulting you can cause distractions by launching a rock in a way to draw a guard's attention. If you are setting up an ambush you can set up jars of oil as to use flame on them or other types of objects and use catapult to start launching them from all over the map to fool them into thinking you have a larger number of people than you do.

In terms of the Magic Stone argument (since that was a week-long flaming spitfire capital-A Argument amidst my group...)

Magic Stone does not create "Damage Rocks" that passively do extra damage to anything they touch.  To deal the damage of the Magic Stone cantrip, the stone must be propelled by a sling or a flinging hand; the damage of the cantrip is the extra force imparted by the magic augmenting your throw.  Using magic pebbles as the ammunition for Catapult, first of all, requires that your 'pebbles' weight at least one pound.  yes, the technical definition of 'pebble' allows this, but players are going to have to keep those ready to hand.  

Second of all, the damage from the Catapult spell overrides the damage from Magic Stone.  RAW, because the prerequisite for Magic Stone's damage is not being met (i.e. ranged attack made with a sling or a throw), RAI because the stone is already being magically propelled and the more powerful augmentation wins out.  As a DM, I would allow as Magic Stone'd pebbles used for Catapult deal 'magical' damage (yes, technically the spell already does so, but it's come into question in our games), but you don't get to, as one of our players tried, catapult a small baggie of all three stones from Magic Stone to add 3d6 to your 3d8.

Similarly, propelling a flask of oil to damage a target while also dousing it for ignition is a cool use of the spell.  Propelling a vial of acid or a flask of alchemist's fire (or, in one particular awesome case, a stick of dynamite propelled at an enemy already on fire from the flask of oil propelled last turn and switched on by someone else's Firebolt) is also a neat function of the spell.  People using Catapult to combo-play with their allies that way are making your game better and more fun, and they should be rewarded for doing so.

Propelling "a case engineered specifically to contain exactly five/ten pounds of breakable acid/fire/whatever" is treading on metagaming and is absolutely cheesing the rules.  They are making your game worse and less fun.  In the case of the players we were having this argument with, the whole deal was "the rules need to be CONSISTENT!", and it vexed them enormously that the DM was arbitrarily ruling that some things worked and some things didn't.  Munchkins and Mechanical People will protest every time because to them, there's simply no reason why they can't throw ten vials of acid with Catapult and get a ton of damage, but the answer these two got was the same one I'll give anyone else.

Sometimes the needs of the game outweigh strict adherence to imaginary physics.  Catapult is already an excellent utility and mixed-offense spell with many interesting and handy uses, well worth picking up.  It does not get to also be the best non-Animate Objects damage spell in the game.

one could say that the multiple damage sources don't stack as a rule. so 5 vials of acid would still only do 2d6 as it is still only going to hit the same surface area with the same amount the extra would simply not effect him as his body is already saturated with acid. and bare in mind the spell can only do 1-5 pounds to begin with if im not mistaken. and don't forget alchemy takes time maybe they guy only has 2 vials to begin with and he's got work orders for his guild, health potions and other things hes got to keep stocked so it bottle necks the amount they have to use; acid is 25gp a piece which can add up then suddenly demand it up and supply is short now the price goes up as people begin turning it into a a weaponized commodity. THEN suddenly its illegal to purchase acid altogether without  a writ from the king or an alchemists guild because someone attacked the prince *honestly it was probably the party* with this catapulted acid and now black market acid is double the original price and not as effective as its watered down. a funny bit of  economic rp for your world all over an attempt to game a lvl one spell.

If someone tried strapping two or more vials of acid I would not have it do all the damage that it could possibly do if they were separate, but more than just 2d6. I'd make it either increase the dice size from 2d6 to 2d8, or possibly just to 3d6.

Off topic from OP, but in topic for catapult spell.

I’ve always found it as a higher success rate method of using your “Grappling Hook”.

Quote from EightPackKilla >>

Off topic from OP, but in topic for catapult spell.

I’ve always found it as a higher success rate method of using your “Grappling Hook”.

 Infiltration, or making your own Thorn Whip when you have Druid/artificer envy, and the barbarian wants to yank things closer.

nets are also only 3 pounds and within the spells perimeters. now that i think of it it only states a weight (5 pounds) but never a size?  so you could  catapult a fully unfurled net.

I wouldn't vary the amount of damage, but I would let you vary the damage type (acid for vials of acid, fire for alchemist's fire, etc.)

Quote from uthidar >>

nets are also only 3 pounds and within the spells perimeters. now that i think of it it only states a weight (5 pounds) but never a size?  so you could  catapult a fully unfurled net.

 

 
It's worth noting that the net would also take the 3d8 damage from Catapult, which would almost assuredly destroy it.  You would effectively be blasting a target with hunks of hemp, not nettapulting them.