[Deus Ex Verra]

Well I'm in the same boat as you but my budget is a bit bigger and I'm willing to tackle an engine swap (in fact I want to, yeah im crazy). Most people will tell you that that's more trouble than its worth though and you're better of getting a diff car with the engine you want.

For 1k you want to look into Air intakes, Programmable ECU (if its cheap), ignition wires/plugs/coils, possibly exhaust (such as headers, performance Cats or mufflers, leave the pipes alone) but that could get expensive quick.

Also lightening the car would help a lot. Speed is all about the lbs/hp or lbs/tq ratio. If you're not worried about sound insulation you could rip a lot of that out, take out the back seat if you rarely use it.

For 5k you could do forced induction but I think you'd be better off sticking to a quality intake kit, good exhaust kit, Performance Cams, Programmable ECU, Performance Clutch if its a manual. Also consider dampers/struts/springs and the like to improve the ride of your car. A properly tuned stiff suspension can make a world of difference, even on the straightaway. (at the very least stiffen up the rear).

And don't forget general maintenance stuff like filters, belts, making sure all the gaskets are sealed properly, fluids are "fresh" and full, all the hoses/tubes/etc are properly attached, etc.