The thing I am sure that everyone tells you is to SKATE, SKATE, SKATE! However, I will modify that slightly with the recommendation to get a book like Laura Stamm's Powerskating and try and do the very basic balance and edge drills for beginners (it's at the beginning of the book). Do them slowly and don't do it for the whole session (have some fun and get some exercise too!) because what most people don't tell you is that if you want to skate fast/well your core/balance has to be quite good otherwise it will be really hard to develop any sort of technique.
Adult classes can be good but that really depends on if it is suited to your level and expectations. You really need to try them out and like you are doing get reccommendations. As long as you are moving a lot (instead of standing around) then it can't hurt you because any ice time is good ice time.
Lastly, learn about hockey. Read/watch videos on basic breakouts, tactics, defensive play. Watching the NHL is really fun but they do things so fast it is hard for most people to understand exactly what happened until they replay it in slow motion.