I'll second the plug for the T-amp. I used one of these when I was sick of the lame computer speakers that I'd previously had. It's got enough power to drive a pair of conventional 2-way bookshelf speakers that I put next to my monitor. For filling a larger room with sound, though, you may find that it doesn't quite have enough power.

(Aside: the clever part of the T-amp is that it's using one of these new class D amplifiers. That's often incorrectly interpreted as "digital" but it's really just a switching power supply, in much the same fashion as what's running your computer. Class D amps, as a rule, tend to run radically cooler than traditional amps, consume far less power, and tend to be very, very accurate in their amplification. Of course, you get what you pay for. Don't expect miracles from a $15 amp.)

The next step up is probably a low-end Panasonic receiver. The Panasonic SA-XR55S (Amazon link, $199) also has a class-D amp and, as you can see from the Amazon reviews, does a very competent job. Most important for you, it will happily digest the digital output from your Squeezebox, and you don't have to worry about putting the Squeezebox on top, as it's not a space heater like traditional amps.

That consumes about half of your $400 budget. $200 is enough to get a semi-decent set of two-way bookshelf speakers. As you might imagine, this is a very personal decision, and there are huge numbers of vendors competing for your money. As a first cut, you should sort out where you want your speakers to go in the room, particularly whether they'll be up against a wall, in a bookcase, or whatever else. This will help you decide either for or against various features. If, for example, you're actually putting your speakers in a bookshelf full of books, then the last thing you want is a rear-facing port, even though it might sound better in the store when it's sitting a foot out from the back wall. To pick a random example, you can get some basic JBL two-way speakers (Amazon link, $128) or even some larger, floor-standing models (Amazon link, $193). Of course, you can spend arbitrarily more money on speakers.

My advice for speaker shopping: burn a mix CD with tunes you know well, pay a visit to your local, snooty audiophile stereo shop, and start listening. You might be able to get a great deal on "last year's model" or even used gear (sometimes resold on consignment) that still fits the budget.