There's quite a lot of budget computer audio threads in the computer-as-source forum, so look through the archives there.
Common recommendations are:
Swan M200 active monitors - these are powered studio monitors, so they need no amplification, you connect them direct to your sound card. They're fairly large, but reportedly kick the pants off other "PC speakers".
Cheap amp + bookshelf speakers. There are many interpretations of this combo. The Sonic Impact t-amp has many adherents. It's a very small, very simple amplifier; it doesn't have a bunch of inputs and outputs, it has tiny spring loaded cable connectors, it doesn't come with a power supply (you can buy one from Radio Shack or Parts Express, or you can run it off batteries), and it doesn't put out much power at all (15W, most people recommend not driving it above 5), but within these limitations, it provides extremely good sound for almost no money (about $30). With an efficient pair of bookshelf speakers it'll be loud enough for close-range listening - you wouldn't want to use this setup for a block party, but for personal listening it'd be fine. There are many possible speaker choices; the Paradigm Atoms you mention are well-regarded, as are the Paradigm Titans. There's also Athena's old bookshelf range which you can buy at a heavy discount online -
http://www.audioprods.com/clearance_...6aece9fb4eb5e4 (that's the Canadian currency link, you can switch to US). There are many other possible choices which you'll find discussed in the computer-as-source forums.
A new soundcard would be a good idea, too; depending on how much of your budget you spend on the amp and speakers, you could look at a Chaintech AV-710 (about $30) or a Creative E-Mu 0404 ($100). For gaming you'd want to go with a Creative X-Fi, but they're not too cheap.