The others have you on the right track, needed - deferred - maintenance on one of these is extensive, but if you do it they're generally reliable cars. I've owned two and had no real issues with either one.
If you get it to run and decide to keep it, I would def replace those lower control arm bushes, check the sway bar mounts for looseness while you're in there - and the ball joints.
Put the car in service mode (remove the front end - plenty of YouTubes on how to do this) as it gives great access to everything you'll need to do. Pull the supercharger and change/replenish the oil - you can really only do this off the car. Check the serpentine belt or just replace it and look at the tensioner and idler pulley. Check the crank pulley too - it's rubber mounted damper will fail, the best solution is the aftermarket high tech one, but it's pretty spendy. Takes a special puller to remove it - don't try to use the one you have in your tool box, it won't work. If that rubber fails it no longer turns the alternator, A/C compressor, alternator or - most importantly - the supercharger, which as mentioned above also turns the water pump!
Pull the crank sensor off and replace the o-ring. I can;t tell you how many pan gaskets were changed because of this leaking, oil running down to the lip of the pan making people thing it was leaking too. It wasn't.
Be careful changing the oil, some people seem to think that the 22 ft lbs the factory calls for to tighten the drain plug isn't right and that it should really be 200, done with an impact wrench set on "all of it!"
Another caution.....removing the oil filter cannister off the back of the block, don't lose the little spring loaded gizmo, it's not available - also I only used factory oil filters, or maybe Wix. I put a cheap on in once and it failed miserably. The factory ones never did this.....
Pull the handbrake and see if it works, take a look at the rear rotors in particular and make sure there's a even wear pattern. if not you'll need some new calipers, rotors and pads. These are not expensive parts tho
Pull the plug wire for cyl #3 out of the coil and clean the corrosion off, no idea why it's always #3, but it is, and it can make it miss on that cylinder.