I'm a beginner looking to buy my first guitar, but I have pretty small hands and short fingers so that's the main deciding factor in which guitar I pick other than price.

I've done some research and the most reccomended guitars for small-handed people are out of my price range (PRS, Fender Mustangs). Gibsons and Strats get a fair amount of mentions as well, so I narrowed down the Squire Bullet Strat and Epiphone SG as my two options.

The difference between the two in terms of size is that the Strat has a longer scale length (25.5) as compared to the SG's 24.75. The Strat however has a much thinner neck than the SG does.

So my question is, which of the two would be ideal for a beginner/small handed person to learn with: the slimmer Strat, or the shorter SG?
Well, the Brian May Special is 24" scale length...
Sturgeon's 2nd Law, a.k.a. Sturgeon's Revelation: “Ninety percent of everything is crap.”

Why, yes, I am a lawyer- thanks for asking!

Log off and play yer guitar!

Strap on, tune up, rock out!
I'd like to keep it under $200 if possible. It's only my first guitar after all.
Scale length doesn't really matter much in terms of hand size. That has more to do with reach.
And the difference between 24.75 and 25.5 is not nearly as big a factor as guitar body shape and playing position. A flying V for example, will generally require you to reach 4-5 inches longer than similar scales lengths, when sitting.

In your case the only logical thing to do is go to a guitar shop and try as many different models as you can, untill you find one that suits you.
I think it's worth mentioning that a Squier Affinity has closer string spacing, shorter nut, and narrower neck than the Squier Bullet. Also, you might want to look at the Squier Jaguar VM HH. It's 24" scale and sells for about $200 new. It's $100 cheaper than the single coil version for whatever reason. The neck plays really great and it's a really fun guitar for the price.

I learned to play on a MIM Fender Duo-Sonic, 22.5" scale, still really fun to play from time to time.
I wouldn't limit yourself. Learn to play on the regular scales and become comfortable. That way you're not immediately limiting yourself to guitar styles that you will mesh with due to what you're used to.

Hand size isn't a huge factor, honestly. Mingus had small hands, that dude played upright like a monster. It takes a lot of hand strength to pull that off.
My hands and wrists are tiny but I hate thin necks and feel much better with a fat wide baseball neck, so slimmer necks may not be the answer to you.