You "could" run a server at home - either you'd need a static IP for your FIOS or a dynamic IP service (like dyn.com). All that said, maintaining a home server can be a hassle: for reliability you would need long term battery backup/generator for your server, router, and ONT (my power was out for 10 days during Sandy...how long was yours out?), you need to be vigilant about keeping your server software, firewall, etc... up to date, be prepared to handle DDOS attacks, and there are many other issues.
If you're really eager to test the waters with your own server, an inexpensive approach would be to get a VPS. You could run a dozen small WP sites on a 1024mb Nginx based VPS server. Suggest you hang out on »www.lowendbox.com/
for a while. You'll find plenty of deals for $5-$10/mo. The community on their forum (lowendtalk) is sometimes a bit harsh, but they definitely will guide you towards reliable providers.
Hostgator used to be pretty good for small website hosting... since they were bought out by the Endurance group and moved to the new datacenter in Provo, things have slipped, but Endurance also bought a number of large hosting providers; you'd have to be careful not to sign up with any of them, as they use the same infrastructure and support that Hostgator does.
All that said: with your small number of websites, you won't run up against the inode limits at Hostgator, you will find their control panel (cPanel) much nicer that 1&1's homebrew control panel, they do have phone support (certainly better than 1&1, but not great), and automatically do backups (unless you exceed 100,000 files.) Defiance82 may well be right about there being more reliable hosts, it would be helpful to actually suggest some that are in the Hostgator price range.
FWIW, I manage quite a few Hostgator accounts (as well as other hosting services) for my clients, along with VPS servers at Iniz, IPXCore, and Linode. My comments and suggestions reflect my experiences with these and with FIOS in Warren.--
V-Rtifacts - When Virtual Reality Was More Than Virtual