budget friendly set up? (total newbie)

All you need—and on your budget, all you can afford—are two speakers and some way to amplify them. So you have two ways to go. One is powered speakers,which contain their own amps. Audioengine is a popular brand. Others will no doubt be suggested.

Alternatively, you can get a stereo receiver and a pair of passive speakers (i.e., speakers without amps, which are far more common than powered ones). Keep the receiver budget to a minimum. Sherwood makes models available in the $100 range. For speakers, I like the Infinity Primus series—the largest bookshelf model they make would be a good choice.

When you're ready to move up, the first thing you'll want to do is replace the Sherwood with an AV receiver and add a good subwoofer.

I presume your computer has a sound card with an analog output, so you probably don't need a DAC. If you discover that this is rather noisy you might try a cheap USB DAC. Behringer makes a good one for well under $50.

Not necessarily. Powered speakers will be more expensive than passive speakers, because of the built-in amplification. The Sherwood/Infinity set-up I suggested will run you $270. AudioEngine powered speakers run $200-400. Separates give you more flexibility when it comes time to upgrading. Powered speakers are a good choice if space is at a premium.

I wouldn't get powered speakers. A typical hi-fi system has a receiver, sub (powered), and passive speakers. The Sherwood/Infinity combo just suggested sounds good (though I haven't actually had those brands). But don't don't forget used stuff, especially for speakers, since they don't usually break and people discard perfectly good stuff. Not often premium, but good. Once you've got a receiver, you can get speakers for a song from used stores, yard sales, or by Craigslist. Well, so long as you're not picky about the appearances of the speakers.

For receivers, I like Pioneer (have had 4 of them).