Buying the system piecemeal is definitely a way to go, but if you just want to get something to start with and want it to work with little hassle, I recommend the Onkyo SR-800. You can still upgrade its speakers at a later date, but it does come with some good quality speakers to start with.
Consumer Reports currently has the Onkyo SR-800 as the best "bang for your buck" for a pre-assembled Home Theater in a Box. It doesn't come with a DVD player, so you aren't paying extra for something you won't use. A friend of mine just got one, and he loves it, it's got great sound and is easy to setup and use. It even has a great auto-calibration mode, where you place an included microphone in the center, left and right of the listening area, and the home theater calibrates itself to sound perfect in your specific room.
One drawback, the SR-800 does not output sound over HDMI, only video. What this means for you is you have to hook up the PS3 audio through optical cables to get surround sound. This way you will get Dolby Digital and DTS 5.1 and 7.1 surround. What you won't get are the new "high definition" sound formats that Blu-Ray has, like Uncompressed sound or Dolby Digital+, which you would get with a receiver with full audio over HDMI. But unless you are a true audiophile, you probably won't miss those formats.
If you *do* want to get the high definition audio from your Blu-Ray movies, then the only choice in your price range is the Sony SS2000, which goes for $350-$370. The overall sound won't be quite as good (the Sony's got tiny little speakers so you get really high highs but little midrange), and it's not quite as easy a setup, and only 5.1 rather than 7.1 surround, but you'll get full audio and video over HDMI.