would be easier to shoot for handling like a new 2004 Envoy.
(assuming you already have all the maintenance items taken care of. nothing like the ride of a car on the side of the road which does not run)
I would just make sure the stock components are behaving properly, and replace as needed. (but that is me)
Shocks, Struts, stabilizer bar end links, stabilizer bar bushings, tie rod ends, ball joints. likely some of these need to be updated after 8 years.
I suggest a lifetime alignment before you replace anything, since you will want to have it checked after any maintenance.
also a lifetime balance deal for the tires. if they are new, or fairly new you could have this added. if not, when you put new tires on. balanced and properly inflated tires make a huge difference in ride and life of the tires.
Also a close check on the brakes, with attention to the back(inside) surface of the disks. they can rust up and give the braking action a shudder.
Prices from Rock Auto on higher end alternatives:
$100 two rear shocks
$260 two strut assy (will compromise spring matching, but I cannot tell the difference, and much easier to do)
$50 stabilizer bar end links front
$10 stabilizer bar bushings
$150 lifetime alignment
before spending more, I would check the status of the gas pump corrosion, find out if GM would help you if it goes, and if not, plan a replacement. (based on your location, and assuming your envoy was driven locally in the winter in salty roads) that would bring you close to your budget.