I just can't believe you will ever see acceptable performance from a home connection with the requirements you have.
The forums are a dealbreaker as far as most webhosts are concerned. They will host you untill your forum(s) begin to utilize too much of the servers resources and then you will be required to upgrade or your acct will be suspended. (usually upgrading won't even be an option for a large forum with many active users, I have seen this time and time again)
So I believe a dedicated server is in your future. Here are two of the least expensive dedicated servers you will find.
ServerPronto Their "starter" plan has a low monthly price but there is a setup fee.
Server4You Same setup fee, slightly more expensive, and only worthwhile if you can pay the yearly advance payment
but You could charge friends/others to host their sites because of all the bandwidth you have available or even split the cost with someone. I think this is the better way to go if you can do it.
Both of these require you to manage the server yourself. Managed servers cost considerably more.
Also, both of these providers get acceptable reviews on the
WebHostingTalk forums which is pretty much
the place to research web hosting.
If the cost of these is prohibitive then you can post your requirements on that site in the "requests" section. You are sure to get plenty of responses, just be sure to check out any host before you go with them.
Honestly, the home connection wouldn't even be a consideration to me.