The way that I play, I tend to get several challenge log bonuses each week simply for playing how I like. I don't chase them down or anything. What I get are:

Complete 10 Unique fates
Get Gold victory in a fate in 5 different regions
Do 3 dungeons
Do 5 dungeons
Hand out 5 commendations in Duty Finder groups
Do 5 leves with different cards
Do 20 leves.
Companion 20 kills (unlocked at level 30) (only gives xp to companion though, not you)
Companion 100 kills

Okay, I actually generally don't do 20 leves unless I'm focused on leveling a job quickly, and sometimes I forget to run around to enough places to do 5 fates around the world (though it generally takes less than half an hour if I do chase it down — fates are always up and generally easily soloable, after all).

For gearing, I found that between running a dungeon a day (that 1st time daily bonus is HUGE — half a level or more up to about 30, then about 1/3 of a level up to 50. And I just got 270K with my level 55 SMN last night out of a need 1.5 million, so still about 15%) and getting dungeon drops then filling holes with GC seals at the quartermaster kept me in pretty good stead. Maybe occasional visits to the market board, since the high-quality white-border gear is still perfectly acceptable and usually not terribly expensive. My gear level average was usually 2-4 levels below my actual level though, since the jewelry items only seem to upgrade once per 10 levels, so they're drag the average down until they'd upgrade and then boost it.

On evenings when you do have time, do low level dungeon roulette. The dungeons themselves are worth lots of XP, and the roulette bonus is a huge amount of XP (and seals, which will be useful later). If one if you is a tank or healer, you will have a very short wait, too.

Of course do your guildhest roulette. That is fast XP/seals.

If your gear is that far behind your level, you may want to hit the market board and see if you can find some reasonably priced stuff to help you catch up. People in guild might be able to craft some proper level stuff too. That gear disparity is probably why you found the FATEs hard.

When I was leveling Rue as a Conjurer I also encountered the same issues and found a great help in the Challenge Log. Obtaining weekly goals of 3 roulettes, leves quests and guildhests helped me build the XP, obtain new gear (from both dungeons and blue treasure coffers in levequests) as well as start giving me a better idea on my rotation as both a DPS Conjurer and as a Healer overall. Hopefully it'll help you do the same for you and Chaide. 😀

Make sure you've unlocked it. (http://ffxiv.consolegameswiki.com/wiki/Rising_to_the_Challenge) Basically, it is a set of weekly goals that will incentivize you to do varying pieces of content. 3 roulettes, 5 leves, some guildhests, etc. If you complete those, you get a nice little bump of xp along with the xp you got getting to that point.

Roulettes are important for this too. Dont forget you get a bonus for doing 1 per day! Between those two aspects and a few sidequests, the levels will come rolling in. Promise!

Dont get discouraged. And don't forget there isnt a 'wrong' or 'right' way to play this game. I know the excitement of those jobs is tantalizing, but don't stress too much on the goal and enjoy the journey there!