Generally you can launch anywhere from Rasta Beach in the north to South beach (in the south

) On light wind days it's often (but not always) windier up North so worth checking the wind meters. On high wind (big El Norte) days, many launches have significant shore break. I've seen people injured from foil mishaps getting into/out of the shore break. In my experience, Playa Central is the place to launch in these conditions.
Regarding the OPs gear rental question, specifically for winging, there's gear to be had but most (all?) of it is older stuff. I like riding a mid length but I've never seen anything like that shape for rent in LV. The boards for rent tend to be of the wider variety in a range of sizes. Moreover, rental fees aren't cheap. This doesn't suit me so I BYOB.