Basically, like the others have stated, the Oklahoma City parking situation is all pay. Since the Bricktown district was revitalized, all of the parking is really expensive close to the station. If you're willing to do some walking to the western side of downtown, you might find some less expensive parking.
I've always gone to Norman to catch the HF, and, while I miss about 20 miles of scenery in the OKC area, the absence of hassle in Norman is great. The parking lot is indeed right by the tracks, next to busy business area and the Courthouse. The station is remarkable in its restoration and hosts concerts and art events from time to time. Also, if you arrive before the station opens, there is a covered patio area on the north end with a scenic garden area to the north.
I've called the Airport Express taxi (blue van), and they've picked me up at my home (about 10mi outside of OKC) and taken me to the Norman train station. Although they don't typically do that, they're more than willing to travel there. These taxi drivers are super courteous and are usually a great way to start a trip.
The Norman train station does have free coffee, and there is also a great diner a few blocks east on Main Street, and I usually get a homemade egg sandwich and milk to go, just in time to catch the train.