I recently traded in my '03 PT Cruiser, so I k now a little about them. Mine had a differnt engine than yours, but that only meant I had to make sure to be a little more meticulous WRT the maintenance.
Whenever you buy/inherit any vehicle, the onus is on you to check it out. Don’t take it to some dealership where they’re going to clean out your wallet just because they can, but instead do a little work yourself.
The air cleaner (a large, plastic box in the lower right quadrant of your hood…open it and look inside and pull out a pleated paper filter) should be checked. Replace it if it is noticeably not white anymore, or even just for good measure. New ones are about 13 - 20 bucks.
Do an oil change on it. You can buy all the tools you will need for under 20 dollars (a couple wrenches, an oil filter wrench, and an oil catch tub) and the supplies (oil, filter) should cost less than 20 as well. If it’s been sitting that long, there’s likely some water and other contaminants in the oil, and it doesn’t hurt to flush them out. You’d spend just as much having the oil sent out for testing, so why not just replace it?
Check your trans fluid (actually not sure where that is on yours, but it should be a yellow hook under the hood that doesn’t say “oil” on it. When the car engine is warmed up, shift from Park to D slowly, and then back into N (chock the wheels so the car doesn’t go anywhere) then pull the trans dipstick out. wipe it onto a WHITE paper towel or cloth. If it’s bright red, it’s good. If it is reddish brown, it needs to be replaced. You can do this yourself, but it’s probably better to have it done. Because Chrysler transmissions are VERY VERY picky about the fluid type they use, this is the one service I would recommend having done at the dealership. It will run about 150 from the dealership.
Replace the spark plugs. They’re about 6 or 7 bucks for new copper plugs and they change out easily if you have some tools.
Enjoy your PT Cruiser. Thewy are very versatile cars for their size. I hauled a dhishwasher home in one, and you can fit 8 foot lumber in there are well if you fold down the front passenger seat.