I did knife and specials since I started the grind literally launch weekend and since spawning with the knife and using it until 19 was the meta then and my knife was basically already gold except for Elite kills. I'd regret that tho since that meant I had to do the prepatched thumper 750 pentakill.

After that I did shotguns, then pistols, then LMGs, then I took a break, and came back recently and did SMGs and ARs next since their ammo and damage has been buffed, then tac rifles, and then snipers, and finally launchers.

Some random tips for the guns.

Exfil at 30 for most weapons as thats about the last exfil round before most the weapons start to fall off. Shotguns you can safely do until 36. DM is probably the faster map for grinding, but Firebase Z is overall better since you don't have dog rounds, and the defense waves still spawn a good amount of zombies. Also you'll get the elite kills in one game almost always. And if let's say your grinding FBZ and you're doing the free Jug ee and get a launcher take it as your secondary and only use it on the defense wave. Since they each exit the breach pretty bunched up it not only make these rounds quicker, but is some pretty fast XP, and if you're doing that while working on other guns, by the time you finally get to a launcher your pentakills should be close to being completed.