Would I be smart to just go that route?
Like Hash said, you could always buy a complete rifle, but if you plan on taking everything off and upgrading, it's better to build it that way from the start.
If you want to, I would suggest building the lower and buying an assembled upper as Wick suggested. That's what I planned to do until I found an assembled lower with the trigger I wanted already installed.
I think a trigger is the main reason to build a lower. Besides that, it's personal preference.
Is that Colt really worth spending more for?
Colt is the bee's knees but if you only want a rifle for fun and don't plan to go to battle with it, anything will work. Just keep a supply of GOOD magazines around - ditch the metal ones and buy Magpul Pmags or Troy Battlemags.
A Bushmaster is also a fine rifle. I have a DPMS upper on a Rock River lower and as much shite as people talk about DPMS, my rifle is unbelievably accurate. Granted, it's a 20" upper and not a 16", it will outshoot just about anything. Don't listen to the trash people talk about certain brands if they haven't given them a chance.
One other question. Core 15 has complete upper .22's.
You can buy a .22 conversion for your AR15 for about $150-200. You simply pop out your bolt and put this bolt in. And you have to use the .22 magazines. Image: http://ts4.mm.bing.net/th?id=I.4571804529198351&pid=1.7&w=202&h=140&c=7&rs=1
It won't be as accurate as a dedicated .22lr since the twist rate is not optimal, but for general plinking, it's tons of fun.
Hopefully I gave you some good information.