what is the benefit of the extra storage? Just for downloading lots of apps?
Yes, for downloading lots of apps, but some other benefits too.
tvOS puts caches a lot of data, which is helpful for going back to a game you were in the middle of playing without it reloading, or going back to a streaming app that you were in the middle of a movie, and you want to continue watching it.
It you check how much free space is on the ATV4K's built-in storage, don't believe the numbers, as it always includes the cache. As you open more and more apps, the OS will free up the cache to make room for the newly opened or used apps.
I plan to use only a few apps
You will be perfectly fine with the 32GB ATV4K. That 32GB will go a long way.
But.... Don't believe the posts that say it is "impossible to fill a 32GB ATV so the 64GB is pointless." I have filled a 32GB ATV4k.
Also, even if you don't fill it, I have noticed that if you open a lot of apps in a short period of time, and there is a fair amount of stuff saved on the ATV, there is a slowdown. This happens even more if you just recently downloaded a bunch of apps.
But... if $ is an issue or if you found a good deal on a 32GB ATV4k, I would just get that. Otherwise, if paying full retail, the 64GB is just $20 more.