Step 1: maintenance - oil, fluids, wash, get your SES light checked if you've got one. Timing belt is our biggest enemy here as well, definitely get that checked. It seems you already did this, but putting it out there.
after that you can really take it any way you want to. If your body and paint is fine (lucky you) you could realistically skip that for awhile until you want to go the route of paint, wrap, or body kits.
In terms of performance the big thing with the GT is replacing the intake manifold and throttlebody for better ones, typically a 2000s hyundai XG350 or 2000s Kia Sedona intake manifold, while utilizing the diamante throttlebody. Check your local pic'n pulls or junkyards with an inventory catalogue. Forced induction is technically possible, but the reliability of the 6g72's stock internals seem to be up for debate on how well they can handle boost from what I have read. If you really want boost, I would suggest looking into an engine swap for a 6g74/5/5 mivec first, since those already supply plenty of power. Search forums for that topic.
For exhaust, you could theoretically go with ebay options which will sound bad but different than stock, or you could invest in a nice setup using an invidia or magnaflow kit. I went with an invidia kit, but my flexpipe was toast, so I straightpiped the car from the downpipe to the tailpipe. Keep in mind you have catalytic converters on your headers, so be sure to mention that if you intent to have a shop handle the welding like I did.
Coilovers or lowering can be accomplished with an angle grinder if you want the classic turbo cheap way, the cheap ebay way, or nice way with some nice megan racings or a KYB AGX + tein combo, which seems to be popular. Check the forums for recommendations. You may be okay with stock rideheight, I personally am not. I'm currently hunting for used parts from older members or considering a gift to myself if/when I land a new job.
Wheels are up to you, stock GTs come with 17'' wheels, alot of people have moved up to 18s which I plan to eventually as well. I believe you Ideally want 8-8.5 width with around 30-40 offset. Just remember stock wheels on coilovers is infinitely better than aftermarket wheels on stock rideheight.
Apart from all that, theres not much I can think of that doesnt fall under personal preference little stuff like headunits or lighting.
Welcome to the club, look forward to seeing your build!