I would first check for leaks, that would be my only priority because if it has internal engine problems then you may have to chalk this one up to experience. If you can't get it to stop consuming oil after all leaks are fixed, you may just want to start saving your money for a better car and drive this one until it craps out but first I would look for leaks.
Experience is what we learn with age, here's what I know:
Upkeep of a used sold car is the BUYER's responsibility!
The seller don't care, it's outta here, all he or she has to (and wants to) do is make sure it's not falling apart and clean it up but beyond that the seller has no responsibility because their responsibility goes to the car they are buying next, see how that works?
Somebody has to take car of the car, the responsibility could fall either way but it makes the most sense to dump your resources into the car you're buying since that's what you will be using, and if all buyers always assume this responsibility then the seller is absolved and it makes it easy, plus it's the way it is
- So, it is always the buyer's responsibility to ensure upkeep, especially with used cars.
It may not be the best news, but it's the way it is, houses are the same way.
ALWAYS change the oil first thing anytime you buy a used car.
Matter of fact you really should splurge at this point and spend some serious money doing a trans fluid and filter change, then replace fuel and air filter, spark plugs, wires, cap and rotor, pcv valve, breather cap, maybe the 02 sensor, also inspect brake pads and while you're there grease pack the wheel bearings and check tie rod ends and bushings for wear... Beyond this a cooling system flush and fill might be helpful but more than this fix and repair anything else that's broken.
Might take a week or two, might cost a thousand or two (far less if you DIY) but it's a long time trouble free driving and thus well worth it.
Bonus: This initial maintenance spell helps wear off that new car excitement, one hates to do it but it's a productive way to wear it off and helps make the buyer respect the car more early on as well.
............
Any car that uses more than one quart of oil between changes is losing a significant amount of oil! Technically speaking no oil should have to be added between changes, thou one quart is considered acceptable... Via this math a car could lose (use) up to two quarts between changes, one quart is added at 1500 miles then at 3000 it's changed, but not beyond.
They all darken some, if changed every 3k the darkening should be minimal.
If after 1-2 changes it still goes pitch black between changes a motor flush might be considered (sold at auto stores in a quart bottle with instructions, or you can use a quart of kerosene if you know how to do it already).