Well, I don't think the third class is just for bored endgamers. It adds utility to all your classes, if you pick class combos that have good synergy.
Which class you pick as third will depend on whether you prefer rogue or mage as your main class.
If you prefer rogue, scout is optimal. R/S is easily in the top 2 dps combos, but in that case, you may wish to start over and pick a different third- mage has limited utility to a rogue. M/R is quite good in PvP, and while R/M has niche use as a PvP rogue, r/s is better at PvP and PvE.
If you choose mage as your primary class, you could pick up warrior, and have a good PvP combo (m/r) and the best PvE combo (m/w).
If you would rather go straight utility, you could pick up druid but... neither r/d nor r/m is really a viable endgame rogue. Both are niche PvP combos.
If you are really hankering after a combo that can heal and dps, I would start a new toon, and do m/p/s (human) or m/d/w (elf). Both those combos have excellent synergy; m/s is an excellent PvE mage, p/s (in mage gear) is an excellent PvP'er, and geared for healing is also an excellent healer- m/p is the absolute easiest mage to level, and can be played successfully in endgame PvE and PvP. M/D also levels easily, and is beastly in PvP; M/W is the best PvE mage, and D/W can heal (if geared for healing) and has a beautiful party buff that melee classes die for.
Mages and healing classes have excellent synergy because they both wear cloth armor, so they can share gear all through leveling. At endgame, you can off-heal in hybrid gear (a few heal-statted pieces combined with your regular mage gear and weapon), or make a whole new set and do two things depending on what your party needs.
There are a few melee-type classes that work well with healers- priest/warrior or druid/warrior for example. You could do druid/warrior/rogue (which gives you druid/warrior and warrior/rogue) or priest/warrior/knight (you could do priest/knight, priest/warrior, warrior/knight, knight/priest etc). You'll need separate gear for each class though.
Some class combos work very well together and others don't. Rogue and Mage are kinda hard, but it's doable. Scout would happily bridge the gap between caster and melee, and work well with both, but you would be sacrificing heal utility.
I really appreciate your insight here, and detailed response

This helps me a great deal, although it was a bit hard to follow haha
I want to ask though, is a warden a good "gap filler" just like you said a scout was? I feel the warden can buff my Mage or rogue class, and that would be really nice.
With the issue of no healing, is it truthfully that crucial to be able to heal, if I have 3 classes made for quite a bit of damage and DPS? Would you recommend having a healing capability for later in the game, or will I lay fine if I do plenty of damage being a r/s/m or r/wd/m?