you may find that if beer gives you heartburn or indigestion, wine will do so far more. that was my experience, especially with white varieties.
the only drink that would not give me heartburn was a good whiskey.
if you are set on wines ... stick to the sweeter or middle of the road reds. The US seems to have some decent reds.
If you can get it, try a South african pinotage ... very unique varietal that only seems to grow well here ... look for the Kanonkop estate, they do export and are excellent producers of it
I have found that I personally have experienced this at times as well, but this is a personal thing and doesn't apply to everyone equally.And, expanding on what I wrote above, I would also recommend red wine to start as well just as our friend has here.
I would probably tell you to shy away from Pinotage to begin though, but that's just my opinion. Pinotage is a great wine... after you have developed a taste for wine and it's characteristics. Pinotage to an inexperienced wine taster could be kind of dirty/earthy tasting and smell kind of chemically. This ISN'T a bad thing! These can be desirable characteristics of wine, but for a newbie wine drinking it's probably not a good introduction. Just my opinion though.
A good introduction to red wine would be one of the many Beaujolais offerings; a region in France known for it's light, fruity, easy drinking red wines.