The Remington R5, Vector and MTAR-X are considered the best and are used often by the pros and every MLG try hard ever. But the Honey Badger, AK-12 are also strong in the assault rifle class, in the SMG class, the Bizon is fantastic for close range, and the Ripper is considered quite strong. If you're into sitting in a corner with IED's and a thermal sight like a massive scrub, the M27 is your go to gun. But it's really all to preference, because the guns are for the most part, balanced so choose whatever you like the best.
As for IED's, blast shield I believe it's called will help with that by reducing explosive damage, but if you don't want to equip a perk to counter them, jumping/crouching/proning will reduce the damage dealt by the IED. Although if the IED is placed at certain positions and angles doing those things won't work and blast shield will be better.
Leveling up is actually pretty quick, I found myself smashing through to master prestige quite fast, but doing operations, and playing certain game modes will level you up quickly. Cranked is believed to be very good for fast leveling.
Can't argue with anything said above. I main the honey badger, it has controllable recoil I think and the built in silencer helps keep you off the radar. With extended mags and a grip it's accurate and you can generally take out 3-4 in one clip. The iron sights are nice.
The ripper is a beast with a muzzle brake.
Cranked is good for fast levelling IF you can get a few streaks going, otherwise playing objective games for objectives.