Redmages just have a harder time pre-41 to get invites, because right now, just about everything you can do in a party, some other job can do it better. You can heal, whitemage heals more. You can nuke, blackmage nukers harder. You DD, you're best friend's grandma hits harder.
Only thing you can do right now better than anybody else is enfeeble, which is often overlooked at lower levels, for a variety of reasons. Powerlevelers for one, for what does it matter if a goblin whacks the tank harder or weaker, PL will take care of the damage, or tank themselves with cure spam.
If you like it, hang with it, because at 40 with Convert, and 41 with refresh, you'll be beating the invites off with a stick. Redmage is a slow blossomer, starts off average, the whole "Jack of all trades, master of none" philosophy. But it really comes into it's own, later on.
As for a rdm, you'll either have /blm or /whm (best to really have both ready) while you exp. Most do rdm/blm, and really that's all you'll need. At 75, when you begin merits (which for you will still be a ways off, but looking to the future never hurts) you'll be asked to be rdm/whm.
Just remember to gear yourself appropriately for what you need to get done, Int+ for blackmagic based spells, Mind+ for whitemagic (important ones being Slow, Paralyze, and Silence). Mp+ and hp+ to get the best 1:1 ratio for convert when you finally get it. If you're going to DD, make sure you macro in DD gear for meleeing as to actually make it worthwhile, and macro in mage gear when you cast.
Either way, good luck and have fun.