Don't even think about using public transportation. OKC, like most cities between Chicago and California, has a skeleton system of public transit. In addition, the only way to get a cab is to call for one and wait about 20 minutes.
Rent a car. You rarely have to pay for parking.
OKC is one of the largest US cities (considering its area, not its population). Because it's so spread out, there is almost never congestion on roads but you may have to travel 5 or more miles to get from place to place.
Trust me, use a car!
Oklahoma City has an original (but run down) bus terminal downtown at 421 W Sheridan Ave. Trailways, Jefferson Lines, and Greyhound port at the facility.