Q. What do the crafter-related attributes Craftsmanship, Magic Craftsmanhip, and Control each do?
A. Among recipes in the game, there are those for which the rate of progress and chance of success are increased by higher Craftsmanship, and those for which they are determined by Magic Craftsmanship. Control helps to reduce the occurrence of aetherial sparking (see below), and exerts its influence over both types of recipes just mentioned.

All recipes, however, have set attribute requirements. Attempting a recipe with attributes below those required will result in lessened progress and quality, even for successful actions.
Source: http://lodestone.finalfantasyxiv.com...f271d7a0a84d5f

Discipline of the Hand
The effect of attributes on synthesis is limited. When attempting to craft a high-quality item, however, the likelihood of success increases as the attribute most closely associated with the tool being used rises. As the attributes associated with the main and off hand tools of each class are different, players may wish to give careful consideration to the class on which they wish to focus. A list showing the attributes related with the main and off hand tools of each class can be found below.
Source: http://lodestone.finalfantasyxiv.com...5e1bf4ab725f29

Q. What type of attributes and stats are best for crafting classes?

A.
Attributes themselves have little influence over the progression of an actual act of synthesis. The higher the stats on the tool being used to craft, however, the easier it will be for the Quality value of the synthesized item to increase. Though results vary from recipe to recipe, a higher Quality value means that a synthesis attempt is more likely to produce either a high-quality item,* or a high-quantity yield.

Also, as the primary and secondary tool stats are different for each Disciple of the Hand class (see list below), it is important to focus on those associated with the class that you most wish to develop.**

* High-quality item names end in a numeral, such as +1 or +2, and possess higher stats than their normal-quality counterparts.
** Allotted bonus points can be reset and reassigned from the Point Allotment interface.
Source: http://lodestone.finalfantasyxiv.com...54e0866aa89b46

This is all that SE has officially stated as far as main/offhand and stats go. Officially, there is no correlation between the logical tool to use and success or quality. Some recipes use craftsmanship, others use magic craftsmanship. At this time we really don't know which use which or what crafting disciplines favor which.