>>1291366pro mechanic here, you need a few supplies to keep your bike in top shape but not much in the way of tools.
basics to keep your bike running well:
-chain oil such as tri flow and rags to wipe down the chain after oiling (once every two weeks)
-bike pump with reliable air gauge such as a joe blow sport. pump your tires up once a week, more often if they're skinny road tires
-two plastic pedro's tire levers
-spare tube in the correct size for your bike
-rema patch kit
-chain checker or 12" ruler to measure chain wear. get a new chain installed when yours reaches .75% of stretch.
if you want to make your own adjustments on brakes, derailers, saddle and handlebar position, or replace wear parts like brake pads, a few more tools are needed:
-if you have a newer bike that uses socket cap screws, get a good quality 2mm-10mm metric hex key set from bondhus, wera, or wiha
-if you have an older bike that uses hex bolts, get a cheap set of metric wrenches, 6 to 17mm. tekton or pittsburgh is fine. gearwrench is a bit nicer.
-good quality 5 piece screwdriver set from felo, wiha, wera, or klein. should have ph1, ph2, and small/medium/large flat head.
-cable tools, chain breakers, cassette lockring tools, cone wrenches, bottom bracket tools, truing tools, and other specialized equipment can be bought as needed, but it's often more economical to do these advanced repairs at a bike shop or community bike kitchen.