You are going to need a fused 4 guage power wire (red wire) running from the positive terminal on the battery through the firewall, through your car, into your trunk (or wherever u have ur amp mounted). It is important to use a fuse and most amplifier installation kits will come with a fuse already installed on the power line. I would recommend these because the power wire comes already secured to the fuse box, so that would be less work for you.
After that, you will need to find a place to run your 4 guage ground wire (brown/black wire). I have mine running to the negative terminal on my car battery. This ground wire will be fed through the firewall along with the power wire and connected to the ground lead on the amp.
The only thing left to power on the amp is the remote wire. You need to find a switched power source that turns on when the key is turned and vice versa. Most carputer power supplies have an amp turn on lead, so you can simply use that if ur power supply has it...otherwise you can go behind the dash and find the turn on wire that used to go to ur now removed head unit.
After you power the amp, your gonna run speaker wires to all of your speakers. This is simple, just make sure that positive goes to the positive connection on the speaker and that the negative goes to negative.
If your gonna prefer best buy as a location to get ur subs from, than ur going to be limited to rockford fosgate and alpine. I'm not sure if there was a third brand, but I know they are very limited in their speaker selection. You should find the speaker you want from best buy and then see what you can get elsewhere for the same price. You'll probably end up finding a better deal on your own than you will at best buy (even after all the discounts).
Your inside speakers are aftermarket and aren't half bad. You should start off with an amp and see how that sounds before getting a sub. I wouldn't recommend trying to power your subs and speakers off of the same amp unless u get an extremely low power sub (which wouldn't be worth it). IMO, you should just go with a four channel amp for now and get the subs later. You might end up liking how the speakers sound and not getting the subs...who knows.