Most new cars come with a matnance plan already. My car was a CPO and I payed a little extra for warranty/matnance. If I remember correctly, it gave me a full inspection and covered all belts and fluids that need replacing every 22k I think. Honestly, Your best bet is that little book that came in your glove box. It holds the answers you seek. Generally, I would look for worn belts (if the metal band is showing or braiding is loose, it's bad), make sure break fluid is top'd off (I mark my break fluid level on the bottle, less fluid means you have a leak), check radiator fluid, all washer fluids, oil level, trans fluid check (burnt smell bad), break pads, tire tread, all signals and lights, check AC and recharge of needed, new air filters as needed, battery check.... You get the picture.
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