I'm about to enter new game +, and I'm wondering which difficulty is easier to take on first.

well, um, Zealot, obviously...but, if you finish Hardcore you get the hand cannon ^__^

You can't do New Game+ in Hardcore mode, so... zealot wins by default.

Do Zealot first. If you want to be as familiar with everything as you possibly can be for your Hardcore run, and you're going to need to play on Zealot separately anyway if you want the achievement.

Yeah, you can't do a New Game+ on Hardcore difficulty. I would do zealot first, since I don't think even after your second play through you'll be burnt out on the game. I'm on my seventh or eighth go (I think, maybe more) and I'm still playing it. The problem with Hardcore though, is that if you can't stand playing the game for too many hours in one sitting, you probably won't want to even try Hardcore, that's my problem.  
 
It's really not that hard, but if you do die accidentally by making one dumb move... well you know. You pretty much have to remember the game perfectly and test things, like what weapon to use in certain areas, and remembering when and where the Necromorphs come out. Like I said, it isn't really that hard, but there will be a few small aspects that may make you dislike it. Go for it after you finish Zealot and see if you'll really want to get through it.

Thanks! What are the best weapons to use during the playthrough on the new game+ of zealot? 

@tvekrules: Depends who you ask.

@big_jon: What do you prefer then? What works for you?

@tvekrules: While I kept other guns on me so I could upgrade them, I stuck almost exclusively to the plasma cutter.