Some really good advice in here from some really good crafters. (Estellios made my Jade Crook! I want it autographed!)

As a much more amateur crafter, here's what I'd recommend:

1) Like Estellios said, when you're leveling, focus mostly on Standard synths.

2) Save Careful synths for the end. Use them ONLY if you've got plenty of Durability left. Increasing your Quality gives a nice XP bonus, but Careful synths burn a lot of Durability. You'll have to play around to figure out where your comfort level is, but as a general rule of thumb, when your Durability is less than 25, you might consider just using Standard to complete the synth.

3) Abilities are extremely helpful in crafting. Before you start crafting, equip your crafting tool, and then go into your "Abilities" screen. Equip any Abilities from any crafts you think will be helpful. When I'm leveling, I tend to focus on abilities that guarantee success for synth attempts. Sepherick's got a great list of some of the most useful Abilities for leveling.

4) More on Abilities. Like most things in FFXIV, you'll want to spend some time leveling all your crafting classes a little bit. (FFXIV generally refers to this as "horizontal" leveling -- which refers to leveling several classes at the same pace -- as opposed to "vertical" leveling -- which refers to leveling only one class at a time.) If you can get all your crafting classes to level 10, you'll learn several crafting Abilities. Those Abilities can then be equipped on every crafting class. For example, if you get to level 10 Blacksmith, you can then equip Maker's Muse on every class. Maker's Muse guarantees the success of the next 3 Standard synth attempts. That's 50-75% Progress guaranteed right there. Once you've learned it, you can equip Maker's Muse on Weaver, Armorer, Alchemist, etc. (Just don't forget to go to your Abilities menu and equip it before starting to craft.)