I assume that two sets of speakers in this 6-speakers system are a woofer and tweeter in the front. I can think of the following possibilities:
Standard front+rear+sub setup:
This involves a set of front component speakers (separate tweeter and woofer) using their passive crossover boxes, and a set of rear coaxial speakers. There are several possibilities for the amplifiers:
1. (easiest to install, budget option) Single 5-channel amplifier powers all speakers and a 2ohm subwoofer (or 4ohm dual voice coil subwoofer wired in parallel for final 2ohm impedance).
2. One four channel amplifier to power the cabin speakers, and a mono amplifier to power subwoofer. This is more expensive, but better if you intend to run something like a 1000watts to your subwoofer, as 5-channel amps can't do that.
3. One relatively high performance 4-channel amplifier uses two channels to power front speakers, and the rear channels in bridged mode to power a 4ohm subwoofer (or dual 2ohm voice coil wired in series). Rear speakers continue to use the car's stereo amplifier.
Simple audiophile setup:
You use a head unit with an _active_ crossover capability, such as Pioneer DEH-80PRS or Clarion CZ702. A single five-channel amplifier is using full range channels to power the (relatively high end) front woofers and tweeters, and sub channel for the subwoofer. Rear speakers are not used. There are variations of this with regards how many amplifiers you use and how to arrange them. I use DEH-80PRS with its auto-tune and some additional manual tweaks. This sounds much better than conventional setups.
Of course, there exist more sophisticated setups, which also cost a lot more, but I will stop here. My preference is the last option, which has the best promise for good sound quality, specially imaging. I understand that this is not always a good advise for a beginner, as it can be costly and one needs to get the head around the concepts such as active front stage. In the light of this, I would recommend to look into the very first setup. 5-channel amplifier powering front and rear speakers and a subwoofer. This is simple and cheap(er than others). I'd recommend to look into an affordable but well built Class D 5 channel amplifier, such as Alpine MRX V70 or Polk D5000.5. Class D amplifiers are very small in size, so easier to install in a compact space, and run just warm (as opposed to often burning hot Class A/B amps that take twice the space). If you're not satisfied with this, you could convert this setup into active front stage setup later on. A typical 5-channel amplifier will give you 300-500 watts on subwoofer channel, which is plenty to fill the car with sound with the right subwoofer. If you can fit a 1cu ft sealed box, you could go with a 12 inch subwoofer as long as it is an appropriate subwoofer for this box size (a lot are not). For 0.5-0.8sealed, a 10 would be better. 12 inch subwoofer will give you a bit more SPL due to large cone area. Another option is Alpine's SBR subwoofer. It's Alpine's 8 inch Type-R subwoofer in a ported box fabricated by Alpine for this subwoofer. These have very good sound quality, and being a ported box subwoofer, it can match the sensitivity of a typical 10 inch sub in a sealed box, but give a lot more energy in 30-50Hz frequency region. About 0.6 cu ft total space used, which can fit in almost any car.
By the way, have you decided how to send signal to the amplifier? If you already have an aftermarket stereo, then that's easy as you just run cables from its pre-amp ports. If you want to keep the factory stereo then you need to convert a high level signal into low-level pre-amp signal. Some amplifiers already have input for high level signal. Others need a processor/converter.