Welcome ! As someone on this side of the pond, I can relate. I ended up a Man United fan starting in the 80s. Went to my first game at Old Trafford Liverpool vs United. Back then, Liverpool as I’m sure you know where THE club so a 10 year old me went for United and fell in love ever since.
Others have already mentioned plenty of good info so I’ll just talk about the tickets. If fans are allowed you definitely will be able to score tickets. Best way is if you are in Manhattan same say they are playing, usually you can get pretty good seats about an hour before puck drop by growing various apps like vivid seats, stub hub, etc.
Glad to have you here. Great place to talk hockey!