The easiest weapon banner for me is definitely AR mastery, my 1st banner ever and now I've got more than a dozen of it, the number is still climbing, I find the histscan ARs have the most reliable damage output when playing off host, the projectile-based ones (Striker, Adas) are more effective on host, but nevertheless fun to use off-host.
The 2nd is SR mastery, because I use infiltrators a lot, after one good Plat match with Javlin GI I can usually complete that gun's challenge from scratch, same goes for the BW or Widow, the SR category also has great variety.
The 3rd one for me is SG mastery, don't get me wrong, I love shotguns, but there are too many projectile-based ones(Graal, GPS, Venom) which is less effective when used off-host, thus increasing the difficulty to get the banner.
The other 2 categories, Pistol and SMG are the same to me, I find pistols way more fun to use, but SMG banner is way easier to get, so they have little difference to me, also I tend to use them only on casters, but powers are generally hard to connect when lag kicks in, another reason I rarely use those guns.