There are others much better versed than I am on this, but my understanding...
Adding an amp should usually be your first step. The reason is that right now you are driving your 6 speakers with the ~50W from the head unit. That can be done (of course), but you are basically then running your HU (head unit) at the upper part of what it can put out. That does not create a volume problem--it creates a clarity problem. Essentially, you start to get muddled sound as the HU starts to reach its top end.
Adding an amp provides you with much more wattage, not so that you can hit that top end again, but so that during normal listening you can be sitting at the bottom half of the capacity. The amp will provide the required ~40-50W very easily and cleanly.
Then, as to how many channels you want on your amp, that depends upon your setup and particularly whether you have (or will want) a subwoofer. A subwoofer is beneficial because bass notes require a lot of power to generate properly (envision the big sub speaker as compared to the tiny tweeter--the big one takes more energy to move). As you can imagine, by stripping the bass out from your 6 'normal' speakers, you have removed a big energy load (thus making them work much better on the sounds they are better at making) and moved that energy load to the sub. That is great, but that will usually take 2 of your amp channels to accomplish (you will put them together to get the energy for that nice sub). That then leaves 4 channels left on a 6-channel amp (in my boat, 2 for the 2 front speakers and 2 for the 2 aft speakers). In your setup, you could run 4 speakers off of 2 of the channels. The down side to that, primarily, is that you cannot adjust the balance between those speakers--they will all be adjusted together (and will run at 1/2 the amps, so you will need to have the appropriate speakers for that).
If you go without the subwoofer, then you can run your 6 speakers on a 4-channel (same issues as above) or on a 6-channel (where you can balance all of the speaker sets).
Then, of course, you could do a 6-channel for your 6 speakers, and a separate 2-channel for a sub. Or, you could.... (this is where the possibilities start to get infinite)
Hope that helps some...