If you stay at Lajitas, you will be driving a lot. I'm not sure of the exact mileage to the visitor's center in Panther Junction, but it will take you about an hr. Once you get in the park, it is 45mph and it is enforced.
If you want full hook ups, you will have to stay at Rio Grande village (inside the park) or in Study Butte at Big Bend motor inn/rv park, BJ's or Study Butte rv park, no pool at any of them. Study Butte is 3 miles outside of the western entrance. If you are coming from Marathon, Stilwell's ranch is outside the park to the north east. I've never been there, but most people enjoy staying there. No pool tho and it is close to an hour from Panther Junction.
It's been several years since I was at Lajitas, so I don't know what their pool is like.
If you stay in the park, you can visit the hot springs, which are located between Rio Grande village and Panther Junction. I do need to add a caution, there are people who go to soak in the hot springs in their birthday suits.