mikkyv - congratulations on starting crafting early in your career - I think it is a smart move. Woodworking makes sense given your job plans, but I would suggest you start crafting as a "generalist" at first. Job plans tend to change as people experiment with different jobs. Also, given your current plans, I predict you'll be leveling ninja at some point. Ninja tools are spread throughout the crafting guilds.
It is really quite easy to craft in all the guilds. For example, one of your first products will be stone arrows (the recipes for these ingredients are given at the bottom of this post). You can make everything you need for stone arrows with zero crafting skill. You'll need to make stone arrowheads (goldsmithing synth), arrowwood lumber (woodworking synth) and chocobo fletching (cloth synth) and then combine them into stone arrows with another woodworking synth.
I recommend you copy the first page of recipes of synths for each of the eight crafting guilds. Staple those eight pages together and carry it with you, read it on the bus, keep it near your toilet, be "one" with it. As your crafting skill rises, your "book" will grow by a factor of eight. The number of different items you can craft increases exponentially. Diversifying your product line is the best defense for a tough economy.
What follows are some general crafting tips, and then some synth suggestions to start off with -
Craft in every guild. You can (and should) join every guild. By developing crafting skill in every guild you'll be able to do synths that require skills in multiple crafts (sub-crafts). One advantage you'll have over crafters who level only one craft is that you'll be able to craft the items you need as ingredients (brass ingots, cotton cloth, arrow and bolt heads, etc.) Plus, you'll discover the many ways that crafting in one guild -> feeds into another. What you'll see is that all the crafts intersect like crazy. Leveling one, fits with another, fits with another. You can take all crafts to level 60 - after which you have 40 levels to use for any one, or all guilds (i.e., you can take one craft to 100, 2 crafts to 80, or level 4 crafts to 70, etc. The exception here is fishing - which you can take to 100 independent of what you do with your other crafting levels.)
Create "mules" in each starting city. If you've started in San d'Oria, for example, create two other characters (purchase content ID for $1.00 per month per extra character) and locate those characters in Bastok and Windurst. Eventually you'll want a third mule for San d'Oria (using my example) because you'll be leaving San d'Oria when you get to around level 10-15 (and eventually a 4th mule for Jeuno). Having characters in all three starting cities gives you the ability to buy items from NPCs in those cities (often the cheapest price available), and opens up 7 Auction House slots in each city for selling your crafted products, and gives you need storage space. You will need more storage capacity as a crafter - get used to it.
Always craft using the same character. There is a distinct advantage to being able to craft "in the field." Juices for mages don't stack, but a player with cooking skill can make 12 melon juices using ingredients that take up only 3 inventory slots. Items like leather hides and logs don't stack. Being able to craft those items into stackable products makes farming much more profitable and productive.
Also, there is a crafting advantage for one character to have crafting skills in all the guilds. Lots of synths have sub-craft requirements. Those synths with sub-craft requirements tend to be the most profitable synths. Why? Because fewer crafters have all the necessary sub-craft abilities. Your competition with these products is lighter; and the profit margin tends to be higher.
Start thinking about crafting with the question: what can I do with these crystals? Obviously crafters will buy your crystals from the AH because they use them to make gil.
Below are suggestions for what you can craft with your crystals. As you craft things, you'll get "skill-ups" in that craft (you'll receive a message saying: "Your goldsmithing skill increase 0.1") Below I've noted the level where the synthesis stops giving you skill-ups (note - you'll only receive skill-ups occasionally, don't expect them every synth). Try not to synthesize something that caps more than 5 levels from your current level. Once you've reached the level cap for the item, either move on to a harder synthesis, or choose that synthesis only for profit-making.
You can get many of the items below from fighting things (worms drop flint stones, hares drop hare meat, etc.) On the left of this page you'll see a "Search" box - this is your friend. When you see an item like "wijnruit" which you need to make antidotes, just plug that into the search box, and you see where you can score that item.
What follows has an emphasis on what's available in San d'Oria, if you start somewhere else, you may have difficulty getting some of the ingredients.
So here are the items you can craft with zero skill in crafting:
Stone arrowheads - wind + 2 flint stones = 6 stone arrowheads (goldsmithing-2)
Arrowwood lumber - wind + arrowwood log (woodworking-2)
Chocobo fletching - wind + 2 chocobo feathers (clothcraft-2)
Luan lumber - wind + luan log (woodworking-3)
Wooden arrows - wind + arrowwood lumber + flint stone + 2 chocobo feathers (woodworking-4)
Peeled crayfish - wind + crayfish (cooking-3) (Peeled crayfish is bait for fishing. Using this bait, you can fish up "items" in easy areas with this bait, but see if you can sell on AH for profit. You can fish up tons of crayfish.)
leather bandana - wind + sheep leather (leathercraft-5)
Stone arrows - earth + arrowwood lumber + chocobo fletching + stone arrowhead (woodworking-3) Notice that you can craft all of these ingredients!
Vagabond gloves - earth + cotton cloth + sheep leather X 2 (leathercraft-3)
Vagabond boots - earth + bronze scales + grass cloth + sheep leather X 2 (leathercraft-5)
Bronze cap - earth + bronze sheet + sheep leather X 2 (smithing-4)
Bronze mittens - earth + bronze sheet + sheep leather (smithing-5)
Cesti - earth + ash lumber + sheep leather X 2 (leathercraft-3)
Antidote - water + San d'Orian Grape + wijnruit (alchemy-3)
Honeyed Egg - water + bird egg + honey (cooking-3)
Copper ingot - fire + 4 copper ore (goldsmithing-3) this is a nice synth for beginners because there is no HQ - high level and low level crafters have a level playing field
Bronze ingot - fire + 3 copper ore + tin ore (smithing-2)
Bronze dagger - fire + bronze ingot + copper ingot (smithing-3)
Roasted corn - fire + millioncorn (cooking-2) (only if Sandy controls the Aragoneau Region; then see Antonian at J-8 Northern San d'Oria)
Sweet Lizard - fire + lizard tail + honey (cooking-3)
Pebble soup - fire + distilled water + flint stones X 3 (cooking-5)
Grilled hare - fire + hare meat + dried marjoram (cooking-6) score the dried marjoram for @ 43 gil from either Benaige F-7 Southern San d'Oria or Phamelise K-9 Southern San d'Oria (neither NPC has this stocked all the time)
Sheep leather - dark + sheepskin + distilled water + windurstian tea leaves (rarely available from NPC in Sandy, check Auction House) (or use willow log in place of tea leaves) (leathercraft-2) This is a key synth for leathercraft, smithing and bonecraft -- make tons of these, sell some for profit and keep the rest for crafting.
Crafting is 'da bomb! Enjoy.