I also enjoy creating proofs as a hobby. When I'm doing it for fun, I tend to use Metamath, in particular, the "Metamath Proof Explorer" (MPE, aka set.mm) which formalizes the most common mathematical foundation (classical logic + ZFC). You can see that here: http://us.metamath.org/mpeuni/mmset.html
The thing I like about Metamath is that every step is directly visible. Coq, in contrast, shows "how to write a program to find a proof" - and not the proof itself. So you can see absolutely every step, and follow the details using simple hyperlinks.
Of course, all approaches have pros and cons. Metamath has some automation; the metamath and mmj2 programs can automatically determine some things, and there's been some experiments with machine learning that are promising. However, Coq has more automation, in part because it operates at a different level.
Here's a short video intro about MPE that I made: https://www.youtube.com/watch?v=8WH4Rd4UKGE
The thing I like about Metamath is that every step is directly visible. Coq, in contrast, shows "how to write a program to find a proof" - and not the proof itself. So you can see absolutely every step, and follow the details using simple hyperlinks.
Of course, all approaches have pros and cons. Metamath has some automation; the metamath and mmj2 programs can automatically determine some things, and there's been some experiments with machine learning that are promising. However, Coq has more automation, in part because it operates at a different level.