For what it's worth, I think it sounds reasonable enough! The Red Mage quest giver doesn't really seem to have any qualms with teaching the art to those who have potential (from what I understand.)
A background in Thaumaturgy and Conjury also seems fine. It's safest to avoid White Mage/White Magic and Black Mage/Black Magic, since both of these jobs are pretty special and not universally accepted in all RP circles. Not that I'm saying you have to care about that, but I reckon if you're asking about Red Mage's feasibility, you care at least a little bit!
Hope this helps to assuage any doubts.
A background in Thaumaturgy and Conjury also seems fine. It's safest to avoid White Mage/White Magic and Black Mage/Black Magic, since both of these jobs are pretty special and not universally accepted in all RP circles. Not that I'm saying you have to care about that, but I reckon if you're asking about Red Mage's feasibility, you care at least a little bit!
Hope this helps to assuage any doubts.