appropriate demo tools for asphalt and concrete

My driveway is FUCKED. super fucked. It collects and holds lots and lots of water (multiple compounding issues contribute to this). There are also two walkways to the front doors of the house that are also asphalt. The whole thing is crumbling and sunken. When it fills up with water, it's over 12" deep in some spots. It's impossible to get in/out of the house without getting really wet. The neighbors say the driveway's been like this for 30 years or more. I peeled up a corner where it was crumbling and it looks like an older concrete layer was underneath, and they poured the asphalt right on that.

I want to start tearing out the walkways. What's the appropriate tool? Sledge hammer? Pick? I hope to repurpose all of the leftover pieces on site, so I'll probably want to break them into manageable sizes.

I signed up for a masonry course at the local FFA to learn about patio and walkway building, but it doesn't start for a few more weeks.

This really is a job for machinery.
With small areas I've dug under and used a pry bar to lift sections. Asphalt is easy, it will break into chunks. Concrete not so much. If there's steel in the concrete that will be the most frustrating part. Bolt cutters, sawzall. Moving the chunks is the worst. A driveway is a lot of lifting.
Can you break it up and maybe rent a skid-steer to move it?
Then you'll need a lot of gravel to fill and grade - this is where you'll prevent future problems by managing water properly. Standing water that freezes will destroy anything.

The ultimate plan is to get a new driveway that solves problems rather than create them. My next door neighbor owns an earthworks company and I've been thinking of asking him to come over and do it, as he's got all kinds of machinery, usually parked in his driveway.

Definitely talk to your neighbor. You could also rent or buy an electric jack hammer.
Home depot rents them for 350-450 per week. I think buying one is a better deal, than when you're done with the job, you rent it out for cash or barter.

http://www.harborfreight.com/15-amp-heavy-duty-professional-breaker-hammer-68147.html