If it says 200watts peak, it's most likely 50w x 4 peak, and probably 22w x 4 RMS. RMS is all you really need to figure out.
Component speakers means the mid and tweeter are separate speakers and there will be a crossover to separate the frequencies that each speaker plays. They can usually be fine tuned (to add a little more mid /little less tweeter (USUALLY)).
If you have (4) 6.5" speakers total, and no tweeters anywhere, then you either need to find a place for them to go, or you don't get components, you get coaxials. Coaxial speakers are tweeters and mids in one speaker in a two and
What they were referring to when they said run a 4 ch amp to just the fronts means get a set of components, then run each midrange and each tweeter on their own channel. It's called BIAMPING. It's not common, and unless you plan on spending at least a couple grand on the overall setup (to include sound deadening, DSP, a second amp, then definitely upgrading your alternator), all because you want just a little bit more fine tuning of your mids and tweeters, then that's just not a relevant or realistic suggestion.
You haven't said your budget.
Your cheapest option is to just buy 4 speakers that fit and play on your head unit's power. You can spend about $100, it will be a little better than your factory was. It won't get too loud, but its the cheapest, quickest and easiest thing to call it a day.
If your budget allows it, (lets call it the $300- under $1000 budget) get a set of components for the front, find a 4 ch amp that has the same RMS, then find a set of coaxial speakers at that same wattage for the back, (you can safely be about 10% off either way).
Then figure out your amperage. Its about 8 amps of draw for every 100watts of power (4x100 =400, which is 32 amps draw). You need to figure out what size alternator you have. For most vehicles this wouldn't be a big deal, but for a honda fit, I think it's a safe bet your alternator is less than 100 amps, and depending on where you go with this, it might be a lot. Then if you ever might want to add a subwoofer, this is where we need to plan and figure out your electrical for your end goals before you start spending money. You might be able to get a 130 amp alt, you need to see what your options are on this, if you chose speakers that can get loud. On top of that $300-$1000 budget you might need a larger alternator and the big 3, and now we've added at least a few hundred more to the bill.
Soooo.. What's your budget, your end goals, do you want a subwoofer, what do you listen to, and do you want it to get LOUD?