There's lots of ways you could go about changing your sound. Not knowing your acoustics and setup, changing speakers yields the most dramatic change in the electronics chain. Yes, upgrading wires is a cheap (sometimes) way to tweak your sound. That said, I'd dump the HD power cord you're using as wire, and go with HD sprinkler wire, for an imediate improvement, yes! (best sounding stuff at HD for wire, hands down!).
Still, at this point, if you are not planning a speaker swap(try-out), I'd upgrade the Bryston, as it's just an "OK" sounding amp, not so much top end, not so refined throughout, and a bit warm/fat sounding. It's same as Lexicon amp basically. Others to consider would even be Classe, Parasound, Anthem, Aragon, Krell's ok, McCormack, and other's you could try.
The pre/pro you could and should upgrade to something with newest HD codec's, and latest DSP room correction, yes, like the Audyssey processing, for superb acoustical benefits to the sound of your system.
Interconnects, I'd be defaulting to harmonic Tech Truth Link. Very neutral, clear, good detail, good dynamics, well balanced - better than the Outlaw, for $100/pr used.
And, yes, there's better speaker wires you can chose for more.
AS for your speakers, the NHT line offers some sonically more neutral, clearer, even more extended (if accurate) sounding speakers, with good dynamics. Also, the Dappolito configured speakers are nice and dynamic and strong through the upper bass midrange area, as well as re-inforcing the treble with the right crossover, for a stronger pressentation for movies and dynamic music, with better integration into a room, acoustically (less ceiling to floor reflection issues, for better detail and more solid image - all things considered. Again, I don't know your room/setup). Speakers like NHT's M5's make excellent music/ht monitors, for passive speakers for cheap. That of course, is if you're planning on experimenting with better speakers - and I would, if I were you.
In the budget speaker realm, there's lots to chose from, of course. It just must all balance with your setup, your system, your tastes, and life-style. (your Paradigms are a more traditional stereo speaker, with tweeter on top, which interacts with the ceiling more, which is not usually a strong HT/music speaker choice, with challenging acoustical issues) I would look for dual mid/woofer designs, really.
Speakers like Thiel SCS4's are more refined yet, but not as strong dynamically in a larger spacel, and they're more money.
At any rate, you need to experiment with ONE VARIABLE AT A TIME to really know what you have going on in your system, at any point. So concider. (it's a hobby if you want the most out of it....unless you get REAL REAL lucky with the first shot or two)
good luck
