None of those will be the least bit weed suppressing, and you'll definitely want that I would think. I suggest you start looking at various groundcovering shrubs. A good local nursery should be able to help.

"Invasive" is a term that has a very specific meaning and your usage here is misleading.....I think you mean you want an aggressively spreading GC. That's very different from an invasive one :-)

I agree that the ones listed will not fit those requirements of weed suppression or rapid spread very well. Or even much drought tolerance. I'd look at something like a groundcover juniper, like Juniperus procumbens or horizontalis.

Will look at Juniperus. And by invasive I mean to spread out aggressively by choking out other plants and weeds.

Nothing will choke out other plants and weeds except maybe kudzu, and I'm sure you don't want that. Anything that aggressive, you don't want. You'll have to clean out the area, then plant. And keep it clean until the desired plants establish.