The owners manual and maintenance schedule (often separate documents) give you the important parts. Two often overlooked causes of early car death are timing belt replacement - for the engines that have timing belts instead of chains - and neglecting the cooling system. The cooling system should have a full service at the intervals specified in the schedule; that includes inspecting all the hoses.
Check fluid levels (coolant, oil, brake fluid, and transmission fluid if there is a dipstick for it) at least once a month. It only takes a few minutes to check all four fluids. Air up the tires once a month, too. If you are losing coolant or transmission fluid, get it checked out soon. If the brake fluid is lower than halfway between min and max, have the brakes checked for wear. Your mechanic will probably do it for free - brake shops do.
Don't "cheap out" on service needs; if the serpentine belt has to be changed and it has a spring-type tensioner, have the tensioner replaced with it. If the "check engine" light comes on take it to a mechanic, not a parts store. The parts store can tell you what codes are present but do a terrible job of diagnosing the actual problem. Speaking of mechanics, find a good one and always take your car there, including for oil changes. "Quick and cheap" oil change places have earned their bad reputation a thousand times over. In addition, the mechanic will keep an eye out for developing trouble, like leaks, torn dust boots, and brake wear.
Ideally, put covers on the seats and on the steering wheel (after ten years steering wheels tend to erode if they don't have a cover). Keep the car clean inside and out. I recently subscribed to my favorite car wash and have found the more frequent washes and vacuuming greatly increased my pride of ownership, the amount of care I give the car. If the paint scratches or chips down to the metal, touch up the spot right away to prevent rust.
Proper maintenance is not terribly expensive and is certainly a whole lot cheaper than trying to band-aid a car that has been neglected.
One more thing: if it is your first car, it should be a used car. *Always* take any used car you are serious about to your mechanic for a pre-purchase inspection before committing to it. If the seller won't allow it, walk away. A pre-purchase inspection costs you about $100 and can - often does - save you thousands on unpleasant surprises. Right now there are over a million "flood cars" (cars that were deep in flood waters from the hurricanes) scattered across the country. They will never work right again and will fail completely before long. An inspection will show that immediately.