So I've recently started playing a Goliath Fighter who's going to be a Rune Knight(we're likely hitting level 3 next session or the one after). Our party is short on arcane utility magic, so I'm toying with the idea of giving my guy a little Wizard flair. My primary intent is to add some of the basic low-level rituals like Detect Magic, Identify, Comprehend Languages, Alarm probably Find Familiar, that sort of thing. So naturally my first thought went to the Ritual Caster feat(probably not taken until Level 6, though). That'd also give me the ability to learn higher-level rituals like Leomund's Tiny Hut, Water Breathing, and even Rary's Telepathic Bond eventually(I'll be checking with the DM to make sure this plan is at least feasible in his world). I also thought about possibly just taking a level in Wizard, I'd get access to 1st-level rituals as well as some reaction spells I could use with my spell slots in emergencies like Shield, Feather Fall or Absorb Elements. And I'd get a few Wizard cantrips along with, some for utility and one or two as ranged options since he'd still be primarily a melee fighter. As I started pondering, I could even take as many as four Wizard levels to get some 2nd-level spells like Misty Step or Mirror Image, probably going with the War Magic tradition. But those Wizard levels would mean I don't get access to the higher-level rituals like Tiny Hut and Telepathic Bond. 

I'm curious what you folks think about those options, if you'd focus on the upper-level ritual spells with the feat, or go the multiclassing route for some actual spell slots & non-ritual magic.

If all you really want is the ability to cast ritual spells, I'd just go with picking up the feat.

On the plus side, as a Rune Knight, since you can use Giant's Might as a bonus action (not a spell) if you are a 3rd level wizard you can then cast Enlarge as your action.  This would mean medium to large with Giant's Might then go huge with Enlarge. Action Surge. Grab the dragon around the neck for Grapple attack and knock it prone.

I woudn't multiclass for just a few spells you'd be delaying all those extra Attacks and that other sweet sweet fighter stuff(and flushing a few HP down the toilet.). If you're just going for the rituals then go for ritual caster.
Another way no covered here yet is letting go of the Rune Knight and go Eldritch Knight. You'll get a bit of Magic (Shield, Absorb Elements spring to mind) and a few other goodies. You could just reflavor those spells as "runes" you use. I one played a tattoed Eldritch Knight with all her spells being Tattoed into her skin.

Quote from Falconcry >>

On the plus side, as a Rune Knight, since you can use Giant's Might as a bonus action (not a spell) if you are a 3rd level wizard you can then cast Enlarge as your action.  This would mean medium to large with Giant's Might then go huge with Enlarge. Action Surge. Grab the dragon around the neck for Grapple attack and knock it prone.

 Not sure if that's how it'd work, since the wording is "If you are smaller than Large, you become Large". It might work like Barkskin, where it just establishes a minimum, without letting bonuses stack on top of it.

Quote from 6thLyranGuard >>

If all you really want is the ability to cast ritual spells, I'd just go with picking up the feat.

 That's kinda where I'm leaning, but the idea of grabbing a ranged damage cantrip(we're a pretty melee-heavy group) and a few spells like Feather Fall, Misty Step, Shield etc. was intriguing. I have a few things I already want to do with my ASI/Feat slots, so I was pondering the idea of delaying those choices by 1 level rather than 4(and maybe taking more Wizard levels later).

Quote from Sutlo >>

I woudn't multiclass for just a few spells you'd be delaying all those extra Attacks and that other sweet sweet fighter stuff(and flushing a few HP down the toilet.). If you're just going for the rituals then go for ritual caster.
Another way no covered here yet is letting go of the Rune Knight and go Eldritch Knight. You'll get a bit of Magic (Shield, Absorb Elements spring to mind) and a few other goodies. You could just reflavor those spells as "runes" you use. I one played a tattoed Eldritch Knight with all her spells being Tattoed into her skin.

 Nope, Rune Knight is who he is, both the abilities and his backstory. EK is still a subclass I'd like to try someday, but it's not this guy.

Quote from jd2319 >>

Quote from Falconcry >>

On the plus side, as a Rune Knight, since you can use Giant's Might as a bonus action (not a spell) if you are a 3rd level wizard you can then cast Enlarge as your action.  This would mean medium to large with Giant's Might then go huge with Enlarge. Action Surge. Grab the dragon around the neck for Grapple attack and knock it prone.

 Not sure if that's how it'd work, since the wording is "If you are smaller than Large, you become Large". It might work like Barkskin, where it just establishes a minimum, without letting bonuses stack on top of it.

 I think it works because you first trigger Giant's Might, which checks if you are already large. Since you aren't, you grow to large. You then cast Enlarge/reduce, which increases your size to huge. Giant's Might doesn't mention anything about growing in size after activation, so I think you should stay at huge. I think it is a pretty neat combo. 

I use the combo on my RK/ artificier but it takes level 8 to come on line.  My Gnome Lott Scang can be any size from Tiny to Huge. 

Quote from JoeltheWalrus >>

Quote from jd2319 >>

Quote from Falconcry >>

On the plus side, as a Rune Knight, since you can use Giant's Might as a bonus action (not a spell) if you are a 3rd level wizard you can then cast Enlarge as your action.  This would mean medium to large with Giant's Might then go huge with Enlarge. Action Surge. Grab the dragon around the neck for Grapple attack and knock it prone.

 Not sure if that's how it'd work, since the wording is "If you are smaller than Large, you become Large". It might work like Barkskin, where it just establishes a minimum, without letting bonuses stack on top of it.

 I think it works because you first trigger Giant's Might, which checks if you are already large. Since you aren't, you grow to large. You then cast Enlarge/reduce, which increases your size to huge. Giant's Might doesn't mention anything about growing in size after activation, so I think you should stay at huge. I think it is a pretty neat combo. 

 It may work that way now, but I wonder if it'll stay that way when it's finalized(presumably in Tasha's Cauldron). Turning a player character Huge seems...excessive.

Order of operation should not change whether two spells/magic abilities stack.

In this case it does as Giant Might on small characters skips medium and takes you straight to large. 

What I'm saying is, activating Giant Might and then casting Enlarge should not make you any bigger than casting Enlarge and then activating Giant Might.

Giant Might

3rd-level Rune Knight feature

You can imbue yourself with the might of giants. As a bonus action, you magically gain the following benefits, which last for 1 minute:

• If you are smaller than Large, you become Large, along with anything you are wearing. If you lack the room to become Large, your size doesn’t change.
• You have advantage on Strength checks and Strength saving throws.
• Your weapon attacks deal an extra 1d6 damage.

You can use this feature twice, and you regain all expended uses of it when you finish a long rest.

Enlarge. The target's size doubles in all dimensions and its weight is multiplied by eight. This growth increases its size by one category-- from Medium to Large, for example. If there isn't enough room for the target to double its size, the creature or object attains the maximum possible size in the space available. Until the spell ends, the target also has advantage on Strength checks and Strength saving throws. The target's weapons also grow to match its new size. While these weapons are enlarged, the target's attacks with them deal 1d4 extra damage.

I think you are missing the point of Giant Might 6thLyranGuard.  If you are not large (ie small) you become large. Then you can go huge with Enlarge.

If you cast Enlarge first you go from small to medium or medium to large. Then Giant Might checks if you are large, which you are, so you stay large.   

The order of operations does matter.  Spells of the same type do not stack however Giant Might is not a spell.

No, you're missing the point.  Giant Might has a clause that prevents it from making you growing above large size.  That effect stays active the entire time Giant Might does.  The only way to get around that limitation would be to use a spell or effect that explicitly changes you to huge or gargantuan size by itself.  Enlarge does not accomplish that.

I see no such clause in what I copied from the UA above. Are you talking about the clause about having enough room?

However, rule at your table as you see fit. We will see if something is different in Tasha's.

Have fun.