I built a home theater six months ago. I tell everybody I did it on a shoe-string budget, which is nearly true. Offbrand TV on a deep sale, used receiver from 2007, used Blu-ray player from 2007. I found a guy selling seven Infinity Primus bookshelf speakers for $30 each. They sound great, even better when put on speaker stands. I bought and assembled the cheapest speaker stands Sanus makes, purchased through Amazon.
You're going about it the right way. Computer speakers are crap, soundbars are crap, and those home-theater-in-a-box sets are crap. A pair of bookshelf speakers and an amp is the right way to go. (Or, if surround sound, many book shelf speakers on stands, or many floorstanders around you.)
Parts Express is trustworthy. I've ordered through them, and DIY builders I know order through them constantly. A lot of the stuff they sell is cheap quality with a price to match. Some stuff they sell is good. I wouldn't consider them overpriced as a retailer. And, as far as I can tell, Dayton is their house brand. So if a Dayton product is sold elsewhere, it is probably sold cheaper on Parts Express.
I think the amp you're looking at is overkill. It's not high fidelity, and those aren't the kind of features you'll appreciate with speakers like that. I know several people that swear by class T amps as being very cheap yet still pretty good. Here is one for $70: Dayton Audio DTA-100a. I've got a friend that knows good sound that got a class T amp for $30. He said the imaging is terrible (when you close your eyes and can locate each "musician" on the imaginary stage in front of you), but everything else is fantastic, and it sounds really great. I could ask him the brand if you like.
Don't worry about how many watts the amp has. Unless you really crank it, you're not going to use more than two watts per channel. Research it if you don't believe me.
The speakers you're looking at ... $30 a pair is really cheap. If that was really my max budget and Craigslist wasn't an option, I'd get the Daytons you mentioned. They look as good as anything.
If you can afford a bit more, look for sales on speakers. Polk Audio makes some really good speakers in low price ranges, and so does Infinity. And the cheap Pioneer series developed by Andrew Jones is really good too.
I bought the Pioneer SP-BS21-LR on sale for $50 and that was a steal. Newegg and Amazon currently sell them for $80/pr. But the prices keeps fluctuating up and down. Check back often, especially Black Friday. Clear and natural sound, bass response is surprisingly good.
I bought the Pioneer SP-FS51-LR floorstanding speakers for $130/pr on sale (currently $153 on Amazon and $150 on Newegg until Thursday, yet Newegg gives you a $50 "rebate card" whatever that means?). Same clear sound, fantastic bass. Almost don't need a sub (depending on your preferences). And since they are floorstanders, you don't need to purchase speaker stands and you still get the best sound! They are a little short for ear-level tweeters while sitting on a couch, but otherwise great.
I bought the Polk T15 for $50/pr online on Black Friday two years ago from Best Buy's website. No lines, no trouble. They are normally $100/pr. It looks like they are $50/pr right now! A great deal. The bass isn't as deep as the pioneers, and the treble is slightly funky, but they're dramatically
better than most in this price range. (My DIY friend also bought a pair and tweaked the crossovers for $6 of parts, and the treble sounds even sweeter. Not as good as his $6,000/pr Magnepans, but stupidly good for the price.)
And anything in the Infinity Primus line is good, although a bit more costly than the other models I've mentioned. Very clear and natural sound, more-so than the Polks. They need a sub less than the Polks but more than the Pioneers.
You didn't mention a sub, but you may want to think about it. I bought the Polk Audio PSW10 from Amazon for $80 on a steep sale once. It is $100 now. I'm not going to lie, it's junk.
But it adds an extra lower octave to your bookshelf speakers, more if you get the Polk T15's. It can handle music medium-loud, or movies at low volume. I've got a pair of them in my home theater now and I listen somewhat loud, and they just fall apart during bass-heavy scenes. But if the price is right and the volume is low...
If you'll have more money for a subwoofer sometime down the road, I recommend Hsu Research (internet direct, so you have to buy through them). From $309-879, you get what you pay for. But you get 1.5-2.0x more for the money from them than you do from any of the other brands. I've calibrated three of their models in peoples homes, and they're fantastic bang for the buck.
More than anything, shop online from home Thursday night or Friday morning. No mess, no lines, but still great prices.
Let us know what you get!