You can't make that distinction for airstrips that are built into the map. If Takeoffs and Landings are enabled in difficulty settings, all Home Bases at hard coded airstrips will be ground start, or vice versa.
To get the airstart Home Base in your scenario, use a Test Runway from the Static Ships menu, and attach your Home Base to the Test Runway. You may have to experiment with the various runways and their placement to force the airstart...I can't recall the exact "rules" at the moment.
Generally, I think, T.R.#4 (the invisible one) will airstart if placed on water, or on uneven terrain. Other ones will airstart only if on uneven terrain, and it doesn't take much uneveness to work...anywhere not perfectly flat over the entire runway extents. Someone can correct me if I'm off on this.
To make the test runways an air start, you must place two runways, but must rotate one so they cross in an "X" or "t" shape (use the keypad to rotate). (and yes, a single runway, placed on uneven ground will produce an airstart as well) (and you should be able to place them on a fixed runway, though I'd set them slightly to the side so you can still land on the fixed runway).
Once placed, you can change both to test runway 4 so they are invisible if you want.
All the above applies to multiplayer "Dogfight" mode maps. For single player or coop missions, simple don't make the first waypoint a takeoff waypoint and the aircraft it applies to will start in the air at the specified altitude and speed for that waypoint.
