The Pioneer amp that should work well with the 8-inch sub should mount in the same location as the stock amp, since it's pretty small:
http://www.amazon.com/Pioneer-GMA3602-2-Channel-Bridgeable-Amplifier/dp/B00GN5K650
Here's the sub:
http://www.amazon.com/Pioneer-TS-SW...1423015491&sr=1-16&keywords=pioneer+subwoofer
You should of course check around for prices, you might find prices at other sites are a few bucks less.
2-way speakers are the simplest and just have a woofer cone and a tweeter.
3-way speakers
usually have a tweeter, midrange, and woofer, but when it comes to the 6x8 speakers, the "3-way" means it has a tweeter, woofer, and a "super tweeter" - a smaller tweeter made for handling the high frequences. Some people regard the design as useless, since the super tweeter doesn't appear to serve much function, but it probably depends on the music you listen to. I'd guess that music with high, high notes like opera and some electronic stuff is slightly better with the 3-ways than with cheap 2-ways.
4-way speakers
usually mean a tweeter, a high-midrange and a low-midrange with a woofer, but again, when it comes to the 6x8 car stereo speakers, it means a tweeter, a woofer, and two super tweeters.
The whole point of having more than a tweeter and a woofer is to give frequences their own dedicated driver, since speakers work better when they aren't trying to reproduce the whole range of sound - this is why theater/concert speakers have lots of drivers, each one for a range of the sound.
That said, 2-ways are more than fine for car audio.
It's worth noting that the 2-way speakers have lower power handling, which actually means they work better when powered off the stereo, where the 3-way and 4-way speakers usually handle more power, so they often aren't as loud when powered off the 14-22 watts each channel of the head unit puts out.
The 2-way Pioneer 6x8's are a great choice for drop-in speakers for an Explorer:
http://www.amazon.com/Pioneer-TS-G6...F8&qid=1423015868&sr=1-3&keywords=pioneer+6x8
I'd suggest those along with two packs of speaker harness adapters:
http://www.amazon.com/Metra-72-5512...23016166&sr=1-3&keywords=ford+speaker+adapter
The adapters let you plug in the speakers to the stock wiring so you don't have to hack up the factory wires, letting you put the factory speakers back if you decide to sell the vehicle without the speakers in it, or just making a cleaner install so you can remove the speakers easily for access when working on the vehicle.
You can of course just cut the stock wires and attach them to the speakers, or just run new speaker wires from the unit to the speakers.