Hello mrforum!
I'm the same as you! Left handed! When I first learnt the drums, my friend taught me to play open hand (left hand on hi hats and right hand on the snare). Initially, there were a lot of confusion especially when I'm trying to do a fill in. For myself, open hand comes naturally because I'm left handed and right footed (I used my right leg to play 'one-leg' when I was in primary school).
Open hand playing means a left handed drummer playing on a right handed drumset. Open hand playing style allows more variation to drumming. It adds more colours but at the same time there are also some usual things that righties can do but I can't. It's usually because of the sticking. Whether I begin with a left hand or right.
If you intend to buy a drumset, you can always mirror the set up so that you will feel comfortable with it. In that way, you are a left handed drummer on a left handed drumset.
There are some lefties that actually play on a right handed drum set normally (right hand on hi-hats and left hand on the snare). It's probably more difficult to start with but eventually you might play like a rightie.
From the feedbacks I've gathered from people, there is no right or wrong with open hand drumming. It's up to you whether you want to play it open handedly or mirror the drumset and play it normally.
Some of the problems to ponder:
1) If you play on a left hand drumset, you will have to make the effort like what chaserr mentioned to move the drumset which is typically for rightie in a studio.
2) If you were to play open hand, the height of the hi-hat can't too high. Or else you will feel the strain on your left hand very soon. Not all hi hat stands can be adjusted low enough for me, personally.
3) If you were to play open hand, you might have to learn to play 16th notes with your right hand. Sometimes you might need it for floor tom (Starlight!).
4) Sticking - Paradiddles can be both RLRR LRLL or LRLL RLRR. I guess open hand drummers got to get used with leading with the slave hand at times.
It really depends on how you want to play. Let me know if you have any questions! I'll help you to the best of my knowledge!