I'm also going to vouch for RDM being a good job to start with. It's pretty straightforward to learn, doesn't punish you much for making mistakes, has nice mobility for a caster, and good utility in the form of Verraise, Vercure, and to a lesser extent Embolden. It doesn't really have a set rotation of abilities you need to learn, rather it's more of a decision tree based on how much black/white mana you've accumulated, which makes it a bit more flexible. The one notable drawback it does have is that it's among the least damage-inflicting jobs out of all the DPS jobs, which makes sense for the added utility you gain. If you like being supportive of your party, mostly in the form of rezzing dead party members, while also dealing a bit of damage then you should definitely stick with it. If nothing else, it's great for solo content as well.

I only have limited exposure to Thaumaturge, so I can't speak much of BLM. But as far as I can ascertain, the basic plusses are nice damage output and essentially unlimited MP once you learn how to manage things between your fire and ice spells. The drawbacks, however, seem to be a lack of mobility and a lack of any kind of raid utility. You're basically taking up the role of a heavy damage turret. A lot of people believe it to be in a bad place atm, but that can always change. If you're into doing pure damage and don't want to worry about your other party members as much, and you're okay with limited mobility, then this is the route you'd want to go with.

In short, I'd actually say try both if you're interested in them. RDM is likely the easier of the two for you to start with, and it'll make the story quests go a bit more smoothly I think. But in the end it really depends on your own personal play style and which sounds like it would appeal to you, and the best way to determine that is to simply try them both for yourself. Good luck, and welcome to the game!