I was not a paddles, but here are some observations….
VFA typically has 3-4 LSO's per squadron. That would include a junior guy who is still working through the UI process, and a senior guy who is normally a wing qual. This manning allows each squadron to throw a body into each wave team.
Selection is both timing, personality, and if yet observed, performance behind the boat. I make that last caveat because most of the time, a guy is ID'd as a new paddles pretty soon after they arrive, and they might well start waving at the field well before the squadron ever goes to the boat. That being said, if that guy ends up sucking, they will find someone else. You need to be at least average, if not a little above average to have the credibility to debrief folks on their passes, which for the most part, ends up being the case.
It's fairly sought after, being a qual that opens up doors in the future (TPS, FRS, CAG Paddles), and I think most folks enjoy it. LSO's absolutely have ground jobs, and if senior enough in the squadron, those jobs can be pretty significant (AOPS, QAO, etc). As for SDO, different squadrons do it different ways, but in a single seat squadron that is pretty body limited, junior paddles often stand no-fly day duty. They won't, however, stand Romeo watch. There is a formal LSO school, located at NAS Oceana. Depending on deployment status, a guy may have been waving for a while in some cases before they ever go to LSO school. From what I saw, it is a lot of OJT.
I'm sure the VFA paddles around here will chime in if any of the above is off base, just observations from a non-LSO VFA guy.