Liberty is the better ship, and cruise line IMO, but we prefer eastern caribbean. Still, I would go for the better ship, Liberty. You will still have fun on either itinerary. If you do western, check out Cozumel Bar Hop in Cozumel. It's amazing! You tour and bar hop on the "other side" of the island, and it's amazing. We will do it again someday.
It' s always acceptable, IMO, but every service member is different. Some like the attention, some detest it. My husband, a retired O5, would not wear his because he would feel the whole night would be about his uniform, and that would make him uncomfortable. Others don't mind. It's very personal, but I feel never inappropriate, and there are many men who go NUTS over it. Your call 😉