Look at synology or one of the other NAS solutions. If you can deal with ARM (ie, not quite enough oomph for docker+vm use) you can get close to $100 price point, and hit all the requirements you mentioned.
However, I suggest forking out a few hundred more for an intel model if you can. My only remaining windows+office instance is now a vm on a 25w box that hosts a half dozen other things. The electricity this saves vs a desktop/home-built server has easily paid for the beefier CPU.
[edit: I estimate this setup is costing something like $20/month, including power + depreciation. Cloud backup is another $10/month, and I run a $1.30 / month cloud vm to host my website.]