Montague: The genetic advantage is always the #1 factor in training gains. My ethnic group/background seems to fall into this problem area. We have been accused of only having to swing around a couple of milk cartons to get bigger arms, back, etc. Not true, first we drink the milk from the cartons.
Probably one of the better systems to jump start the arms is running the rack. Beginning with a pair of 5lbs and working the way up the rack and (here comes the hard part) than working back down to the original 5lbs.. Different version of this, an usually anyone of them work. Also exceptional for the delts when doing sea-saw presses or even lateral raises.
The one & one half systems is another method that can produce gains in arm size fairly well. Though, remembering again, not any system works for all people the same. Even 'roids don't always work for some, giving little or no results. Others grow like a magic.
Yes, chins and/or pulldowns are good biceps movements. Believe Mentzer discovered that idea from Art Jones. Close grip, and try to keep elbows closer also. Check out the biceps of some gymnast, if wanting more proof. Noting the guys who favor ring work. If your gym has exercise rings, than might make use of them. They tend to follow the twist of the wrist/forearms/biceps rather that the fixed position of a bar (chin bar/pulldowns attachments). Twisting has a strong affect on the biceps, because twisting is one of the functions of the biceps. Good Luck.