The above advice is all good, but, optional. Esp on a frugal budget. The biggest problem is GM's exhaust and that includes the "Asthma Attack" turbo. Look at the passenger side manifold pushing the driver's side exhaust past two ports at 90 degrees.

Very few members have fixed the manifold problem. (The results from those that have are impressive.)
Yes a good 4" exhaust with a better down pipe. 4" kitty if equipped. This is in prep for a better turbo.
Otherwise why mess with it? Seriously the factory turbo is simply too small for all but low RPM off road and daily driver, UNLOADED. It will run with the turbo backpressure getting extreme and costing you MPG while dumping the heat into the cooling system. Even the knock off HX40II's are worth saving up for. In other words the gain from a better turbo is bigger than all the small stuff without a better turbo. I feel bad for
@Will L. as space doesn't allow a better turbo for him. Maybe Turbo Resource out of Lake Havasu can build a turbo that would fit?
Long hard pulls are best served by a even larger towing turbo, but, you trade off the lower RPM leaving from a stoplight.
Will is correct: I have attempted to melt down several of these engines with extreme EGT. Didn't happen.

EGT when the ECT is under control is a big unnecessary heartburn myth for this engine. Other engines may melt down at X degrees EGT. Not this engine. 6.5's like yours have a coating on top of the pistons. The 6.2 engine I had didn't have the coated pistons.
It sustained 1550 EGT for miles towing a grade with minimal smoke. The only evidence was a burned turbo blanket. Buddy, who was tuning the engine at the time, was ghost white when I was reading the numbers off and NOT taking my foot out of it. No doubt from having visions of walking from the middle of nowhere. From extended high EGT's I recommend wrapping the downpipe past the passenger floor pan as the exhaust can burn the paint in the area. And the burned paint (both sides) on the floorpan was from 1400+ sustained EGT with a factory turbo for over 10,000 miles towing 550 miles a day up the Mongolian Rim to 7600'+.
The take away from this is:
1) Top piston coatings are for longer oil life. I have shortened oil life on that hot rod 6.2 with an ATT and BD spool valve.
2) Timing is a big factor. Over advance timing and melt any diesel down with low EGT.
3) EGT is a decorative gauge on the dash that tells you how hard the engine is working.
4) You loose control of ECT with hard work... Well you keep ECT below 210 or you have run out of cooling system with the hard work and bad things happen: Scuffed pistons, heat damage to rings that now have high blowby... ECT is related to EGT, but, with ECT under control EGT doesn't matter.
Note: I do watch and limit the EGT's on the Cumapart because it's a different engine with known ways to fail from high EGT like dropping a valve seat.