It's currently a carbed car. This means you've got a lot to do to get it to injection.
I staved off going to injection on my Syncro for some time due to the complexity of the upgrade. What carb does Dec have at the moment? Weber or Pierburg?
If it's a Weber 32/34DTML you need to find out why it's not running well. Is it worn? Are the jets correct? Do you have proper air-feed equipment on it, not some donkey pan filter?
Unless the engine is shagged, before you dive in and tear the engine out, why not sort the handling and braking first?
This means a GTI rear beam, which has the rear anti roll bar stapled on it, as well as the discs.
If you're going to rear discs then you need to add in the brake compensator unit too, so you're into a lot of hard-line replacement, too.
As someone's already stated, upgrading the fronts will give you far more improvement anyway. A modest upgrade to 256mm and a 22mm master cylinder will see you right for now.
I only suggested that someone was an idiot to run carbs when they were proposing replacing their injection system with carbs. Now that would be dumb. K-Jet's ripe for lampooning as various people fete it and it's chronically out-moded these days.
If I was you and I wanted to upgrade your car I'd pick up a 2.0 block, crossflow 8V head, get it lightly breathed upon and tweaked to fit, buy a Megasquirt system, a stub manifold and some bike throttlebodies and make yourself something properly zingy yet simple.
By the sounds of it the OP's already made the sensible decision - buy a GTI to replace his existing car. Provided the engine runs reasonably well then there should be a 17 year old keen to buy your car as a first step on the ladder. Plenty of GTIs out there to choose from.