The only prostrate rosemary I know of is Rosmarinus officinalis prostratus, but there are probably others. I grew this cultivar extensively in coastal South Carolina and love it in hot, humid conditions.

@rhizo what kind of soil were you using?

westes, to answer some of your other questions, you need plants not seed. That would be very hit and miss as regards germination and the quality of the resultant plants. To get a particular cultivar get a plant. I've never notices any difference in flavour between different Rosemaries I've tried. I cant answer the soil question because mine grow in the ground. But you do need something with good drainage.

Rosemary does not require alkaline soil - mine grows perfectly well in our naturally acidic soil. Preferred pH range is between 6.0 and 8.5 so plenty of room for variability. You just want a pretty durable, fast draining soil for any container plantings but I wouldn't be overly worried about the specific pH.

Couple of other cultivars you could look at are 'Huntington Carpet' and 'Blue Lagoon'. Huntington Carpet is very popular in my area.

IME, pretty much ANY variety of rosemary will work well for culinary purposes.