I still have my first-gen SE and it's my primary phone, the battery have started to show its age. I am also experiencing the problems you mention with the home-button being worn out, in humid conditions it will press without me pressing it, I've sort-of solved it by using the on-screen home-button (I haven't found a way to tell iOS to ignore the hardware button).

It's the perfect size of a phone, I've considered seeing if someone can replace the battery and the home-button.