If you don't want to out level the MSQ, then leave the side quests for an alt and focus the MSQ with your main. Only do side quests that are requisites for something you need. Also, I wouldn't worry about being over-leveled for the MSQ. The solo instances and dungeons it throws you into will be level synced. Some solo instances can be quite challenging so being a little above the level requirement is advantageous.

As for gear, the advice given so far is really good. I wouldn't rely on dungeon drops to gear up, but rather use the dungeon drops you happen to get if it is in upgrade to your current slot. I also want to add that your GC also has really good gear that provides bonuses when equipped with other GC gear. These cost company seals which you can get through various means. Also, keep any GC items you purchase on a retainer to use when you level alt classes.

Good luck out there! Perhaps I will see you at the Sunken Temple of Qarn. One of my favorite leveling dungeons!