I foresee two possible issues with your situation:
- It may be difficult to use to right leg to keep you up after you have stopped
- It may be difficult to give a lot of power with your right leg when going up hill
The first issue is easy to overcome. You just make sure you lean a bit to the left when stopping and you use you left leg. Your leg will be almost straight when touching the ground, so it may not be an issue at all. For me landing on the left leg is a habit and I always do it. I only put the right leg on the ground when I loose balance to that side, that happens sometimes because I do not put any effort in to avoiding it.
The second issue is also easy to overcome, just buy a bike with more gears. Then you can always keep the pedals moving fast enough to provide most of the power with your right leg when going up hill. I would recommend 7 or 8 gears, that should be enough. Bikes with more gears usually have two handles to change gear, that can be confusing when learning several new things at the same time. If you like technical stuff you can also buy one with 28 gears, it's not a huge deal to have two handles for gear change.
I know training wheels are generally not recommended, but if you really cannot hold yourself up with your right leg, even when it is (almost) straight, you may want to consider having a big training wheel on the right side only.
One last tip, find a safe place to practice. Not all countries have safe bicycle lanes.