Definitely practice with both hands. There will be a time when you just can't do something with your dominant hand or it's just plain easier to do off hand.
I can now proudly say that I can weld horribly with both hands.
I was just telling a buddy over the weekend that wants to learn to weld better (he just recently started learning) to avoid picking a dominant hand to weld with. I've always tried to switch things up to avoid having to weld at awkward angles due to not knowing how to switch it up. Being sorta ambidextrous is huge for welding.
I’m looking at picking up a multiprocess dual voltage welder like the Miller 215 in the near future hopefully (I learned Mig/Tig/ stick on high end Miller equipment a few years ago, so I’m partial to blue). I’d love to get a Miller 220 that is AC tig capable too but it doubles the price and I can’t justify north of $3k on a welder. I need to be south of $2k for sure. Anyone know where to find reconditioned units? If the kinks have been worked out of a used machine, I have no problem going that route.