A magnetic pickup, like a dynamic microphone, doesn't require phantom power and can therefore be connected to any microphone preamplifier that can amplify the signal enough. Magnetic pickups tend to have high impedance, which not all preamps like, which can result in that the higher frequencies get dampened.
Your noise can be caused either by your computers microphone input being crap (highly likely) or that you aren't using shielded cables (less likely), which you need to do when using a microphone, or because the pickup isn't shielded (also highly likely).
It can also be because you haven't been able to set the levels on your sound card correctly.
In general it's a good idea to invest in an external preamplifier at least in the long run. There are many available with USB or firewire inputs that you can connect to your computer and have a good quality input from any sort of microphone. Many of them have both stereo inputs and stereo outputs and are then usually called USB audio interfaces. Make sure it take high-impedance sources (most do) for your guitar.
If you get a preamp, a stereo preamp. They aren't that much more expensive and it's good to have stereo.