Is painting enough?
Depends how far you want to go.
I would suggest renting a concrete grinder as the easiest fastest method to remove the old coating.
If you drive your vehicle on this floor you will need a two part type garage floor coating that will resistant hot tire pickup. Most retailers (Home Depot, Lowes, and Menard's) stock garage floor kits. Typical kits range in the $100 price range and are ready to drive on in 72 hours. There are also some higher end kits available in retailers now that are drive on ready in 24 hours - While you will pay a premium for these kits they are twice as durable.
You could pressure wash it and see what comes off. Degrease it with a proper cleaner like the ones found in the 5 or 1 gallon jugs at your home store. Then wash again and epoxy it.
Pressure wash with a water/sand system to keep the dust down. That will give a blank canvas so to speak then epoxy or concrete stain.
You could rent a concrete grinder and use progressively finer grit blades then stain/polish. This gives a very nice high end professional look.
Whatever you do I would recommend against any paint. No matter what the manufacturer says. You're in that predicament now. A good solvent based epoxy is much better than a water based one. No matter what you choose to apply surface prep is the key. That means getting rid of grease, oils and stains that would keep the products from adhering correctly. A garage floor is at the top of the list where proper surface prep is essential.
I would steer clear of anything that would require a 30 day cure period. I have used epoxies and stains after 24-36 hours with no issues.
Try to keep a vehicle off for a bit longer or you will have hot tire pickup issues. (Google that)