What? You expect all Canadians know how to play hockey? Jeepers...
Ok, fine, I'm a Canuck and I played competitive hockey growing up, lol.
In addition to all the comments above - regarding your inability to "stop" - I'd have to say you're in a "beer league" (fun league), and there will be no fighting. My guess - you fight - you're suspended.
Maybe it's different over on that side of the pond, but rarely would you see a fight unless it's a competitive game, and very few leagues allow it (typically the higher level ones). And by "allow", I mean you still get a major penalty, but they might not throw you out of the league. It's best to find out the policy for you league first.
Nobody mentioned goalie yet - and if your skating is what I think it is - it might be an easier choice - but probably more frustrating, lol. Winger might be the best - you'll be closer to the boards to help stop, lol.
Not like running at all...well, not too much. Can you downhill ski? That would be a much closer comparison with regards to the weight distribution and balance.
I'd say just make sure you have elbow pads and plenty of padding in the bum. No offense at all - but I'm imagining a LOT of falling down on the ice, lol. The games go back and forth so much - definitely work on your skating as your #1 priority. Crossover turns, backwards, etc. Otherwise it'll be like playing cricket if you couldn't control how or where you jogged to, lol.
My first preference would be a full face mask. You're not at the level where the extra bulk detracts from your speed/skill. Sticks can fly everywhere, and slap shots will knock your teeth right out.
If it's summer over there - consider practicing with inline skates (rollerblades).