I know this may sound harsh but if you don't have time to work on your car because you spend most of your time with your daughter, don't even bother modifying your car. The only real way you can be within budget, and have a strong reliable motor is if you tear down the engine yourself. That means pull the motor from the bay, separating the head from the block, taking these parts to a machine shop, and etc... You don't have to put together the internals, which some shops can do that for you, but the big money saver is taking out the engine and putting it back in yourself.
Here's a run down of parts (this is just high guessing the prices)
Block:
- Machine shop (hone cylinders, tanked, rebalance crank, coated) - $600
- Pistons - $400
- Rods & pins - $300
- Bearings - $300
- STUDS - $200
* I'm sure you can get the machine shop to install these parts as well (if they reassemble) in the price above
Head:
- Machine shop (valved, tanked, porting in/ex, reassembled) - $400
- Valvesprinfs, retainers, etc.. (kit) - $300
- Camshaft w/ gear - $300
- Head gasket - $150
Motor work alone - $2950 (give or take a couple hundred bucks)
Turbo kit:
- EBAY TURBO KIT (mani, turbo, downpipe, fmic) - $700
- Send in the turbo to a reputable turbo shop, have internals rebuilt - $400
- Reputable wastegate - $300
ECU & tuning - $600
Total after all of that... Just about $5000