And as far as I know, getting SDSL or a T1 is gonna set you back a few hundred a month, at which point you're better off getting a dedicated box.
Start with a VPS -- even if 30 bucks a month sounds like a big chunk of change, consider your other overhead (rent, groceries, etc). Not a big price to pay for the benefits.
Good luck!
As for power, you've always got UPS'.
Internet is the tricky one as all private hosts use redundancies, although I don't see why you couldn't sign up for regular internet and a cable connection.
I've seen a handful of ISPs that let you run a server (or more correctly, don't stop you), although I think most ISPs prohibit it to force you onto business packages (which you can get in your home too).
I know in the Toronto region there is Mountain Cable, which doesn't have anything in their Terms of Service preventing you, and have unlimited bandwidth (From speed tests I've seen, they're faster than Cogeco, and get an upload speeds in the 1+MB/s range). I think you've just got to settle with DynDNS, however from what I've read this is reccomended for static IP's too. If you did have two ISPs then this would solve the IP problem when you switch.
I'm actually considering going with Mountain Cable anyway as they're cheaper than Cogeco. Although their lack of information on their website freaks me out; I mean their service area map isn't even online. (Edit: They do have a service area map for their internet, however they apparently provide service outside of the area)