i've also started a new char mate an i find the best way to level is run the campaign while doing bounties, ofc its going to be time-consuming you can't expect to get level 20 in couple hours bro.

im also on 360, gt:dooobie dooo

lv 12 atm.

Crucible games earn you 1800xp if you win or lose in skirmish, that's how I leveled from 15-20 in about 2 hours
If not running the campaign on the hardest difficulty while running with bounties is the other easy way
Or if you have time go do a loot spot and just sit and kill

Have someone level 20+ run campaign with you on hardest difficulty you'll be rank 16 in no time then hit crucible and always do your bounties

I have gotten to level 2 to 20 in 5 or 6 hours.
Method one: Play the first couple of mission so you unlock bounties. Then go get crucible bounties and get to rank 10. After that you can run the campaign by yourself and it will be easy, after u get lvl 18 do the strikes.
Method two: unlock bounties and run the campaign with a lvl 20+ u should get to around rank 16. Then do the crucible bounties.
I have leveled up my character to lvl 20 4 times and helped one of my friends out. (4 times because I deleted my one character because I got to max 30 they were both the same class. )