10 Endurance so you get maximum Hit Points when done leveling (not including Lifegivers). Questions about builds usually depend on how you intend to use that character. So if it's TB PvE or RT PvE, or TB PvP or RT PvP, or exclusively TC or Reno etc matters to me. Not for all.
Also what matters is which weapon specifically. Not just Big Guns, but which Big Gun? Your high PE lines up with Rocket Launchers, or any longer-ranged gun. I personally enjoy PE 1 fighters a lot. PE 1 might sound scary, but i use Avengers and we do the most dmg at 1-hex, thus i don't need the high PE. Even in PvE farming ops, PE 1 starts me in encounters very close to enemy - right where i want to be for a 1-hex Avenger fighter. Not good for Rocket Launcher though ouch.
So ditto to what these guys are saying about Strength. Take ST 6 and plan to use Buffout/Cola, and Psycho. Use beer if PE is 1 and swap basic Toughness perk with Quick Pockets for Avenger fighter. The beer will act like Toughness and QP saves you a lot of AP recharge time. Avengers hold only 3 bursts so that's a lot of Reloads. Add up those Action Points saved over time - it's worth the the perk imo.
When i use Buffout, i always set AG at 10, but if you are patient enough to wait for an Agility implant then register AG 9. Intelligence 1 tells me you are patient already so...good. Your last perk is at level 24 but can be delayed until sometime during level 29, so yes i think you can get BRoF with IN 1 (but use the planner to verify this). +1 to the Small Frame idea to get an extra AG point. Avoid Fast Shot if you want to do a lot of bursting. Avoid Fast Shot if you plan to fire Rockets.
Note: you can get Awareness with PE 1 if you get Close Combat up to 100 which is not hard even with low IN.
Your perk decision looks like you're thinking clearly: which ones is totally up to you, Lifegivers vs Action Boys and don't forget Bonus Ranged Damage. I take Action Boys on snipers but not on tanks. On tanks i take LG and Stonewall, but you could mix it up however you wish: 2 LG instead of 3 and 1 Action Boy plus some +1 AP armor gives you 12 AP! And ditto to what Sperber said about tagging Doctor instead of Throwing unless you are just so eager to throw stuff. Or even tag Energy Weapons but leave it alone until later and look forward to the day when you can choose between bursting with a gatling laser or Avenger either one. Doctor works pretty well at only 100 so tagging it might be medical overkill.
Note: i leveled a 3x BRD BG burster and was so unimpressed with the increased damage vs the lowered HP, i rarely use him.
Hey if you want some specific builds, i can send em but it seems like you are starting on the right track and getting good advice from these guys.