Get a hold of the service schedule for the car. It is usually in the owner's manual or a seperate book, if it didn't come with the car it is pretty easy to search online and find the schedule for almost any care. (In fact here it is:
https://my.gm.com/content/dam/gmownercenter/gmna/dynamic/manuals/2010/pontiac/vibe/2010_pontiac_vibe_owners.pdf) Find where you are now in terms of miles and years and do everything that should have been done by now (since you don't know the history of the car). There may be some things you can skip, but ask yourself what happens if that part fails; an O2 sensor failing might result in the engine running a rich, a failed timing system could result in a destroyed motor.
Looks like maintenance up your age and miles includes:
Oil Change
Engine Air Filter inspect/replace
Cabin Air Filter inspect/replace
(omitting transfer case and rear differential as you are FWD)
Inspect Seatbelts
Inspect Drive Belts
Listen to engine for tappet noise and adjust valves if needed
Inspect Gas Tank/Cap/Gasket
Change Automatic Transmission fluid
I would probably also flush the coolant.
Check to see if any on the shocks/dampers are leaking.
Personally, I would find the date code on the tires (if it easy to determine a quick internet search for the model of time will tell you how) and if they are original or close to original (so ~10 years) I would replace them regardless of how much tread is left on them. Some folks will argue that number should be 6 years.
Check the tires for uneven wear, if you can detect it with your eye ... well it maybe too late. Even if they look fine it might be worth getting the alignment checked.
On the non-maintenance/wear item front. For my own peace of mind I probably would have a trusted mechanic (if you know one) look it over and tell you what isn't perfect and what needs to be done now/what can wait/what you can live with forever. At that age and mileage and without a known service history I suspect there is a thing or two that is less than perfect outside of the normal upkeep (worn/cracked rubber parts/worn out shocks/slightly bent suspension components/exhaust least/leaking gaskets/
Oh and a good cleaning. Every car I have ever owned gets a good wash, at least a light polish, a "permanent wax" applied, a good vacuuming, ideally a carpet/upholstery shampooing (I once took the entire interior out of a car and hosed out this carpet ... it was that bad), and rise/"wash" the undercarriage.
It would not be a bad idea to replace the headlight bulbs. The standard filament bulbs do eventually die, but along the way they get dimmer and dimmer. There is an entire sub-section of the internet where people argue about bulb temperature, brands, lumens, whether LED retrofit kits are bad and if not which ones are good, and on and on.
go to recalls.gov and look up your car. See if there are any recalls that apply (looks like brake problems, sticking gas pedal, melting window switch, and the airbags have been subject to recalls for your car). It may take a little leg work to tell if a recall has been performed. While you are there feel free to scroll through the "manufacturer communications" there are 747 for your year/model. A lot of them point to issues that the manufacturer knows occur and gives information of how to address them should they arise.
