It all depends on how serious you want to do it and what your budget is.
Here are a few different scenarios:

1. Either buy a PODxt or a Digitech GNX3 (or 4 if you can afford one). You don't have to fiddle with amp settings and mics which are not really suited to a home setup. They plug straight into your pc via USB and do not require you to go out and buy an expensive soundcard.

2. To mic up your amp to a pc you will need a proper soundcard. I recently did a LOT of research before deciding which one to upgrade to. If you are price conscious but want something which is genuinely an excellent product, I would recommend anything by M-Audio. Soundblaster are just not made for home media production (even though they say they are). I got an M-Audio Delta 1010 on E-Bay and would receommend this as the best buy for the money. Things to look out for are proper jack plugs (not earphone sized connections - you need to be able to plug your guitar directly into the card), zero latency (good hardware with the latest Asio drivers) and a midi connection for external devices (very important).

3. A crap mic will make a good amp sound terrible. Some amps have a line out which keeps the volume at a constant level (eg Marshall), this can be jacked straight into the pc/soundcard. Sound is ok this way, not amazing though...

My best advice would be to go on to E-Bay and look for a good deal from someone selling their own studio gear. Then you can get a soundcard with good speakers and a mixer OR look for a well priced PODxt or GNX3 or 4.

Best of luck