I’m not sure about 3ds max, but Maya LT has a free, 3-year student license (I’m pretty sure you can just renew it when it runs out anyways) that you can get by simply inputting a few details about what school you go to (they allow “homeschooling” as a school, but their registration page seems to have changed and now I think you have to select an actual school, but you can still just pick any at random, it doesn’t ask for any school ID info or anything like that. Anyways, the content you create in this version can’t be used to make money, and every time you open a scene created by a student edition, it gives a notice that it was in fact created by a student edition, and cannot be used commercially.
3ds Max might also have this, but I never checked. Since you say you didn’t plan to make money off of the game, and because it seems like you’re more trying to learn than to actually sell assets, my recommendation would be that you get a student license and just learn the application that way. Once you get confident and want to actually start making money, the monthly price of Maya LT is $30 (which I know all-too-well if even that is too much to pay). Forewarning though, even if you create assets in the student edition and then later subscribe for that actual program, you are still unable to sell or use the assets commercially that were originally created in the student edition, so you’d have to start from scratch.
I once tried blender way way way back when I was creating content for The Sims 2, and I only had the choice of free programs. I came across Blender and, I thought it was because I was just young, but I hated the program with a passion. Then I stumbled on Maya and always felt at home with the UI. I recently tried Blender again but it still retains the same feel as it did in the past, and I just really can’t see myself ever using or even trying to learn it again. The good thing is that even if you can’t use the Student assets, you’ll most certainly learn how to make them from scratch in the full version once you accumulate enough knowledge. :X