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Cable, your guess is as good as mine as to speed. It varies by time of day and number of users. You're using the cable company's infrastructure. Likely to be good speeds though. YOu might see 500K when things are clogged, or 5mbits if things are going well.
A T1 line I believe is about the same as 26 phone lines. It's also about 1.5mbits of transfer - but it's asynchronous, so you can get that speed both downloading and uploading. However in comparison to DSL and cable, it's slow these days (that being said, it's still way overkill for what's needed to serve a few sites). I think T1's are a bit outdated as there are better ways to accomplish the job if you actually need that size of pipe. A few years ago before reliable and common datacenters and fast DSL/cable they were a better idea.
If you don't have a high volume site and are planning on hosting from home, it really doesn't matter which of those three solutions you need. If it's more than that, you should forget hosting from home and get yourself in to a colo/datacenter somewhere.
>>Is that necessary to run a home-based server off a PC?
assuming it is just a test/home server or something unimportant then you don't need it to run a web site from home, although running a website with a dsl connection will be slower than you might think.
if it is an important website you shouldn't host at home for all kinds of reasons