i take it you have windows vista (since you say it's a new comp)?
i'd probably recommend avast (as well as the others). all you have to do is register it, and you can have it for free for a year (for evaluation). should you consider buying it, it's not that expensive.
anti-spyware, i'd recommend ad-aware (as others have mentioned). alot of the programs (antispyware, etc.) that i have, don't say they work with vista yet. i normally use spyware blaster, spybot search & destroy, etc. (i'm just not sure about vista)
since you are using limewire, i'd recommend purchasing ad-aware (since the free version isn't real time, you have to initiate scans afterwards), or another decent anti-spyware program.
since i have dsl, i use those programs (computer associates antivirus) for free, and i use avast, etc., on other comps (friends), that don't have any antivirus programs.
fyi, since i just bought another comp (not that i needed another one, but the sale was too good to pass up), that is vista, i'm going to find out what all is available for vista. g/l on whatever you decide, sos
oops, i also normally use zone alarm firewall (which you can use for free), just not sure about vista