Sandy's ideas are great! I don't have experience managing the maintenance team, but I can offer some help with 2 & 3:
2) Resident Retention - Love Sandy's idea of a newsletter to introduce yourself. Consider having a mixer so that you can actually meet them face to face and get to know them. I'd also recommend sending out a satisfaction survey to see what areas you can improve upon within your community. Making residents feel like you value their opinions will go a long way towards increasing retention rates. Be sure to follow up with people when you get suggestions, though. Let them know what you're planning to do, but also let them know if you have limitations and can't get something done quickly enough. If you get their suggestions, but do nothing, they'll feel like you just don't care. My strategy for renewal time was to set an appointment to discuss their renewal rate with them. That way I could explain why there was an increase, what we were planning to do in the future, etc. It helped ease the blow and I got a much better renewal rate that way. Carpet cleanings were always a hit, though. Especially if someone was a long-time resident.
3) Leads - With leads, I always recommend following a pretty firm schedule. Respond to email leads within 30 minutes and phone leads within an hour. Prospects that came into tour, I sent an email within 24 hours and always sent a personal postcard the following day. When it comes to prospects who seemed really interested but didn't lease that day, I always tried to call again after 48 hours to let them know if the unit they liked was still available or if there were any changes to our pricing since they left. The hardest part is making sure your whole staff is doing the same thing, though. Since you're new, make sure you meet with them to get everyone on the same page, give them the follow-up cadence you'd like them to adhere to, and run through the previous week's leads to see what steps they should take next. After a few weeks of meeting like this, they should be on a pretty good schedule and should know what you expect.
Congrats on the new position!