First, welcome to AE.
Second, what's the precise version of AE you're running? You'll find it under "About After Effects". If it's the right version, you may be able to extricate yourself from that God-Awful Windows Movie Maker.
Third, yes: an uncompressed AVI would be about as big as you state.
Fourth, tell us about your laptop. Details are estremely helpful, particulrly the amount of RAM & storage, plus the processors and OS... chances are pretty good it's not a great fit for AE use.
Fifth, since you're brand-new, please understand that AE's not the kind of application that lets you do complicated stuff as a neophyte. And don't trust just any old YouTube video. Would you rather learn the basics from high school kids or the pros? There are a LOT of basics that are prerequisite to AE success, and your path to that knowledge begins here:
Good luck on your journey.
This should explain your initial question: FAQ: Why is my output file huge?
Take that resulting file and drop it into Adobe Media Encoder to make something you can actually view on your machine and/or into something Windows MovieMaker can use. Alternatively, ditch MovieMaker and go with something much better-suited - Premiere Pro. Handily, Premiere Pro and After Effects work very well together if you want to add AE's magic to it. (Although, you could do the names title thing in Premiere without using AE.)
Seriously, after you've learned how to use Premiere, you will wonder how you ever did anything with Windows MovieMaker.
And, if you want to learn how to use AE, definitely follow that link Dave gave you. It is invaluable advice.
Edit: I see Todd was faster, but in my defense, I typed more stuff!