Welcome to the club!
The speakers run on generic speaker wiring through the harness. Depending on how much of an audiophile you are there are a bunch of different options to consider.
The least hassle would be to replace the speakers with equivalent sized car speakers and plug them right into the same harness. That won't get you any better sound quality, but it's really simple.
The next option is to run a new multi-channel amp to the speakers. That will take component cables to the amp and then speaker wiring to the individual speakers. You can run some higher powered speakers that way, but I wouldn't go too high powered unless you upgrade the sound deadening material along with it. Basically what Rockford calls their "Deadskin" would need to be lined in the doors and other sensitive areas to get the best results from a new high powered system.
Car audio doesn't generally use coaxial cables, but it depends on the style of head unit you upgrade to also if that's being changed out.
And in case you need it, the size of the speakers are 6x9 front, 6.5 round rear, and 1" tweeters in the dash.