That amp will be a good match for your speakers. You're right in comparing the RMS value of the speakers and amp, that's all you need to worry about. You can use basically any kind of amp for any kind of speakers as long as the amp is tuned so that it doesn't push the speakers too hard.. but the amp you've ordered is a very good match.
The amp probably won't add a lot of clarity at medium volumes, but it will have roughly twice the power of your head unit, and should add a lot of volume and a lot of clarity at high volume. Plus it will give your head unit a break, they get pretty hot when the internal amp is pushed.
You will need an 8 gauge wiring kit, the kit should come with everything you need except for the actual speaker wire. If you plan on ever expanding your system in the future I would go with a heavier gauge kit just so you don't have to replace it again.. I have an 8 gauge kit installed right now, and I just got a second amp so I have to upgrade my wiring to at least 4 gauge before I can install the second amp.
You can get a wiring kit at www.crutchfield.com
, on ebay, or your local electronics store. The cheapest will probably be ebay. If it says "8 gauge wiring kit" it should come with everything you need except for speaker wire. And as for speaker wire, I haven't installed my amp for my door speakers yet or I could give you an estimate.. maybe use a piece of string and pretend to route it where your speaker wire will need to go, add the strings together and a little bit extra. If it was me I'd just buy a roll of 18 gauge wire and call it a day. Haha.
I wouldn't say that your system is 'bottlenecked' by your speakers, you should get some decent volume and clarity out of them when your amp is in.
Right now I'm fighting with running my 18 gauge speaker wire through the rubber grommets in the doors.. it's proving to be a PITA. Might have something to do with the fact that it's usually -15 celcius out though.
Well good luck, if you need help with the install just post, there's probably hundreds of amp installs between everyone on here. LOL