My first bit of advice would be to go shoot a few matches with what you have.
You will probably still want to change, because a longer gas system will give you a flatter, softer, and faster shooting rifle.
Is your upper a flat top or a carry handle? Do you want to shoot with iron sights or optics?
You don't need to spend $1200 for a good 3-gun rifle. But depending on how many parts you will need to change, you may be ahead to just sell your colt and put together a quality budget rifle.
All that aside... assuming that the upper receiver that you currently have is of the type you want to use in the future... all you need is a new barrel (18 inch with rifle gas is my recommendation for an optics upper), with a gas block and gas tube, and an inexpensive comp on the end of it. And a new bolt to go with your new barrel. You can use your current bolt carrier... but a bolt should not be swapped between barrels for any extended round count.
I have had good accuracy and good results with BCM SAM-R barrels (expensive), and DPMS MK12 barrels (inexpensive).
Bolt ~$50
Barrel ~$150
Miculek comp ~$30
Gas tube ~ can't recall
If you have a carry handle upper you will need a clamp on fsb to go on the picatinny gas block that comes with the DPMS barrel.
Otherwise I presume you currently have an optic on your colt.
You could sell your colt barrel on the AR15.com equipment exchange and recoup a lot of your new parts expense.
If you have a carry handle upper and you want to shoot optics you should probably just sell the colt and start over. Get that whole large pin BS out of the way.