Can somebody recommend a really simple recipe for grain alcohol that I can then turn into white vinegar? Is there something I can do with water and sugar?
You would not use grain alcohol to make vinegar. The production of grain alcohol is not legal in the US without a license. The production of such is not allowed for discussion here.
Acetobactor will produce a much more desirable vinegar than any chemical conversion. They also don't tolerate alcohol much above 20% so you're better off using regular wine, cider, mead, or a strong beer.