You might want to look at something along the lines of a Home Theater receiver. The model you listed doesn't have a subwoofer output (from the info on Crutchfield, anyway). That means you'd need to buy a sub with "SPEAKER LEVEL" inputs, and while that works I think you're better off using LINE LEVEL inputs where you can. It give you more flexibility. There's quite a few decent HT models well under $300, and most of them have flexible, powerful bass management that will let you send the bass just to the sub and the rest of the musical spectrum (from 80 or 100 hz on up) to your mains. Denon receivers are very good in this respect as they all do bass management properly, but there are lots of good brands. Panasonic and JVC both make very nice digital receivers that run cool and and are full featured. And both are available for under $300 (actually sometimes under $200). NOTE: there's nothing wrong with the Onkyo TX-8511, but if you want to add a subwoofer you're better off getting a "more modern" style of product.
In all likelihood your current mini system speakers could be made to work with whatever you buy for a receiver, but you're not likely to be satisfied with that for long. Any decent receiver is far more powerful than the average mini system. It's better than nothing until you can buy some new speakers, though. Just be careful with the volume so you don't fry them- especially if you like heavy music (and who doesn't!
).
It's hard to recommend speakers without knowing your budget. However, the Athena Audition series is very good and also pretty cheap. Many Best Buy stores carry them. They don't have much competition at the price, and they may be just what you're looking for. Anyway, if you can let us know how much you can spend, we can give you more specific advice.
A good sub is probably in your future too, from what you say. That will take a load off your mains and give you a lot more "oomph" than you get with the speakers alone.
BTW, the wire you use isn't that important, but I'd suggest at least 16-14 gauge wire. Spring clips are kinda sucky compared to binding posts, but they work. If you do buy a receiver with those connectors you might want to buy screw-on or crimp-on Pins for your cables. Several companies make them and they don't cost very much.