I'm new to the world of recording, so I want to know... what are the pros and cons of recording by computer and recording with a multi-track recorder? I've already dealt with tape recordings, and the sound quality is horrible.

Which way should I go? I want to go kind of cheap, but I was a decent sound as well.
it depends on

A how good your computer is
B the software you use
C the hardware (sond card/other PCI cards)
D your knowlage in computers being high enough to know how to operate the various comonents of the software. you can use $20,000 system and still make a ****ty recording if you dont know how to work it.

and then it would depend on the multitrack recorder you are talking about. computers are allways going to be better in this day and age but some of the better multitrack recorders will be better some of the cheaper PC recorders.

i subjest the line 6 tone port and DONT get the cheap one get the more expensive one (i think there is only a $50 difference anyways.) this should get you started with recording untill you get familier with it enough and you can research the other alternative methods.
also go buy some good computer speakers or headphones.
ESP B-405,Fender American Jazz Bass(EMG J active pups and LEO QUAN BADASS II ) squire P bass(EMG P active Pups)),
SansAmp Bass driver DI
Ampeg SvP PRO Tube Preamp
QSC2450 Power amp
Furman PL8