Getting a vps for $8-$20/mo from linode, slicehost, prgmr, webbynode, rackspace cloud or any other vps provider is so much easier than dealing with a machine at your home.
I have a couple of low end VPS machines with different providers. The liabilities include:
1) If it goes down, and you need it up NOW… there is nothing you can do.
2) It may become inexplicably slow as they move pigs onto your box.
3) Given your low rent neighborhood you may find yourself banned because of your IP range. (I live in hope that someday Comcast will lift their wholly unjustified ban on my email server and my daughter will be able to send email to her great aunt.)
4) Expect more outages than a simple PC. Sure they use "server grade"[1] hardware, but they also have insanely complicated setups. I generally reboot my physical servers when uptime goes past one year, just in case. That is not going to be an issue with the VPS machines.
5) Many packages have a predatory bandwidth overage charge. I've never triggered one, but it is a cause for concern.
6) Storage can be very expensive.
On the happy plus side:
1) When the server goes down, there is nothing you can do. Go have lunch. This beats the heck out of frantically diagnosing and fixing while the phone rings off the hook with people who want to tell you the server is down.
2) You automatically have two sites. Your house becomes "offsite backup".
3) Your VPS probably has much higher bandwidth than your house. (Except you lucky Koreans, and Finns, and Japanese, and.. well a lot of you people with real bandwidth to homes.)
[1] "server grade" means a 100% chance of a high price, and an X% (where X < 100) that it will be reasonable quality. I've purchased and installed batches of "server grade" machines from top manufacturers that had MTBFs under 12 months. By the time you know a model well enough to trust it, the vendor no longer sells it.