don't go thru the mic input.
go thru the line in.
Mic has a preamp, which will color the tone.
Also, don't plug the speaker out to the computer, ur liable to blow the sound card. *giggle*. Trust me.
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Try not to do a lot of conversions (RCA->1/4" etc) it will degrade the quality...but odds are u wont notice it anyway. Just go to radioshack (i assume u have one where u are) and tell them what ya got and what ya wanna do...they'll help ya.
we use CoolEdit, it comes with lots of plugins...one will help to get rid of the hiss/pops u'll get on ur LP/tapes.