CATV distribution is a hornet's nest of compromises. Believe it or not, there are times when passive splitters are preferable to amplifiers. Amplifiers add noise; if you can split passively and still get, say, 0 to 10 dBmV at each receiver, then you're probably better off with the splitters (as long as they're good splitters with adequate bandwidth. Old splitters, which may have been used in your house, are useless above 300MHz or so).
I should point out that a CATV "distribution amplifier" system is usually a one-in, one-out amplifier followed by a bunch of splitters or directional couplers. One thing many DIYers don't know is that it's generally a good practice to terminate unused splitter outputs.
Cable modem is tricky because it uses the sub-band (below channel 2) that many splitters won't pass very well. I agree with previous statements that you should locate your tap-off for your modem as far upstream as possible.
Before you do anything, ask your cable company if they would move your "drop" to a higher-output tap on the directional couplers that feed your neighborhood. It would be better to get a stronger signal on your drop, strong enough to allow you to split passively, than to take a weaker signal and amplify it and then split.
Also, check the coax in your house. Older types of coax and connectors are lossy/leaky compared to modern types. If you find any of that old skinny RG-59 junk and two-piece F connectors, replace them with good RG-6 and snap 'n seal F-connectors. It can make a difference.
I won't even get into setting "tilt" right now, since presumably the cable runs in your house are not very long. But you should pay attention to the amount of tilt on the signal coming in on your drop. Is the reception worst on the lowest channels, gradually improving as you go up the dial?
Hey PRR, you're off dialup now? Congrats! The day I ditched dialup for DSL was a happy day indeed.
Kev, there's an Analog Devices chip that makes a nifty video DA of up to 8 outputs. I was inspired to check it out when I noticed that it's used as the output stage in the new Leitch DAs we used in our truck and MCR. I got a couple of free samples from AD a while back--I'll check on the part # when I'm at work tomorrow.