In securing a wallet, there are some things that you need to do that are applicable to any secure computer. First and foremast, you need a state-of-the-are firewall! This will keep away 99.9% percent of the hackers, their trojans and key loggers. Next, don't download shit unless it is from a reputable source that you can resonably trust.
I cannot emphasize on your last sentence. Better even: Don't
download and install anything on the machine you're going to do
serious Bitcoin trading with. Of course, you'll need the bitcoin client and a browser. But I've seen too many (both linux and windows, but mostly windows) PCs with tons of crap installed. Oh and refrain from visiting your favourite porn site. Don't install Adobe Flash. Don't open PDFs.
At best, use a dedicated PC. A shiny new 300EUR netbook or your 5yr. old Pentium-M laptop should do.