It depends on the system or the character whether I come up with mechanics or backstory first, but you always have to have a concept. Reading on Wookiepedia about different species, such as Gand, can give you some great ideas.
My personal recomendation is to spend all your starting xp on Characteristics. I also reccommend getting as many stats to Three as you can, even if it means taking additional obligation. If you are a human or lunged gand for instance, you can have a 3 3 3 3 2 2 starting array, which is pretty nice. I generally don't recommend spending xp to take stats to 4 at character creation, as it's less effecient. You can always raise attributes later through Dedication, which costs 25 xp. Generally speaking, edge is a game where anyone might be called on to make that charm or negotiation roll, not just the guy with +20 to diplomacy. I personally don't like to have any characteristics at 1 because you're at risk to fail even simple checks (no difficulty).
Generally speaking, characteristics should determine how many green dice you roll and skill ranks should determine how many of them are yellow. The reason for this is simple: it will take less xp to raise the relevant characteristic than to raise the skill ranks of all the skills in that characteristic, as a rule. More green dice are better than smaller numbers of yellow dice (until you get into large numbers of dice where the better results on the yellow dice can even it out).
Remember you don't have to pick your favorite specialization first. Sometimes it's worthwhile to pick one that will give you better starting skills and/or offers a straight path to Dedication. Also, some talents are somewhat dependent on equipment, and you may not have that equipment yet.
Lastly: figure out how you're going to contribute to combat and space combat.
No offense, but this isn't great advice. Well, investing as much xp as possible in characteristics is, but a 3/3/3/3 stat array is garbage. The reasoning is complex and requires some dice math, but let me see if I can break it down in a reasonable length (forgive the cocktail napkin math).
The first important thing to understand is how little upgrading from a green to a yellow dice gives you. Ability dice give a 62.5% chance of success per dice while a proficiency dice gives only 83.3%. This means that, at least from a success standpoint, adding a green dice is almost 3x more beneficial than upgrading. From an advantage perspective, ability dice give a 62.5% chance of getting an advantage while prof. dice give 66.6%. So if you are looking for advantage then upgrading to a prof dice nets you only .4%.
With those numbers in mind, you can start to see that stacking characteristics with skill ranks is only superior to adding a green dice if Triumphs play a large role in skill checks (Example: Crafting, Medicine). Otherwise, the best use of your xp would be to focus some characteristics, raising them quite high, while allowing others to remain low but pumping up their skill ranks.
Under that logic, a skill array of all 3's produces a situation where the player will be investing a lot of xp bumping skills but gaining minimal benefits for most of their early careers. What is better, would be to determine which characteristic has the most skills for your archetype. Invest in that stat and allow the others to remain low. Of course your career skills have to be taken into account because you don't want to have to waste xp raising non-career skills.
Speaking in a general sense, raising Brawn, Agility or Intellect very high is good because they contain a lot of abilities that can benefit from high stats with only a few ranks. Wil, Pres and Cun all have builds that you might want to do that, but it is generally better to leave them low and buy up the 1 or 2 skills you want.
As mentioned, the exception would be crafters or doctor types were triumphs are abnormally useful. In that case, stacking dice is the way to go. Of course with crafters, maximizing boost dice is the way to go, but that's a different conversation.
Combat is tricky, because lots of combat characters care about advantage and by proxy triumphs. Since upgrading a dice does almost nothing to increase your advantage chance, you have to do some strange math to weigh the benefits of adding a dice (5/8's chance at an advantage) with upgrading (1/12 chance of Triumph). Since adding a green also have an increased chance of adding successes as well, I generally lean in that direction but its less cut and dry than something like a knowledge check.