Not first come, first serve. Merely whoever looks like they will fit in with the other characters the best.
I'm normally not a big fan of rolling for ability scores, but I like how random they can be... so CharGen is as follows;
Ability Scores: 3d6
Roll this 9 times, taking the best 6.
Also, new feat;
Combat Training [Jedi Bonus Feat]
Prior to actual combat, you have opted to train concurrently with Republic cadets, learning the organization and structure of the Republic military and a gaining a cursory knowledge of basic soldiering and the daily lives of the men and women who will soon be your subordinates.
Benefit: You are automatically proficient with Light Armor and Pistols (to include rifles with retracted stocks)
You have free access to almost every single weapon, armor, or gear available to the Republic. They will outfit you completely free of cost. This includes upgrades and the services of a Tech Specialist. Specifically templated items cannot be procured, nor can vehicles or ships be freely given.
Jedi volunteers are commonly offered the same gear as the Republic's special forces, usually light power armor and commando special rifles. This helps them blend in with the average grunt and offers them added protection. As such, Jedi Knights accustomed to years of war have made good use of the Armor Specialist talents offered to them.
While on the battlefield, you can generally be assured that your fellow republic soldiers have access to plenty of spare power packs, grenades, and heavy weapons. Occasionally you'll have access to vehicles too. (That being said, the individual mandalorian's gear is vastly superior and personalized)
Edit: If you can find it in a book, you can use it. And if it isn't there, feel free to run a homebrew by me.