I live in a mansion with 17 other students. We have 11 TV's and one
cable modem in the house. We have 1 cable drop coming into the house
that we then split 12 ways. As you can expect, the cable tv looks like
crap. I am looking for someone to tell me the best way for us to
amplify and split this cable 17 ways from one drop (specifically what
products we should use and if we should split from one location or in
multiple locations.

This is not a professional opinion, but I would try putting a two to
one passive splitter on the line coming into your house and feeding
one output directly to the cable modem. Then I would put an amplified
splitter on the other output and use it to feed the TV's. Ideally, you
would have one amplified splitter with all the outputs you need. Since
that is a lot of outputs, you may have to build a tree with, for
example, one amplified 1:4 splitter feeding four additional 1:4
splitters, to get 16 outputs. You might also experiment with passive
splitters and see how much attenuation you can stand before the TV
signal is unacceptable, then build the system using as many passive
splitters as you can get away with. The passive splitters will be much
cheaper than the amplified ones.

If you need to distribute the cable modem to multiple computers, I
would do that with the ethernet connection at the output of the cable
modem, not by fanning out the cable and using multiple modems. The
easiest thing to do would be to buy a wireless base station with
multiple ethernet outputs. You can run category 5 cable to the
connections you want to be wired and use wireless connections for
others.

Please be sure to check your service provider's contract terms so that
you are not doing anything illegal.

I meant to explain why I would not put an amplifier upstream of the
cable modem. The TV signals only need to go one way, from the cable
head end to your TV. The amplifiers will amplify the signal going
downstream, but in general will attenuate the signal going upstream.
This will cause problems for the Internet connection, since signals
need to go both directions.