Like any other military force, cartels are run by their supply chain. As such they use whatever is the most plentiful and easiest to procure and supply ammo for in their area of operations.

E.g, cartels in a middle east/European scenario will most often be using surplus Russian military gear and ammunition, central/south America will rely more on NATO and US calibers imported south, Africa will use a smattering of both European and Russian calibers depending on the local colonial influence, east Asia will be dominated by Chinese and Japanese specs (themselves also often derived from Russian designs). And almost everywhere you will find Russian equipment, they made and sold so so fucking much of it.

Since they are more clandestine that government forces they overwhelmingly rely on small caliber arms that can be concealed and shipped. Not too many mounted machine guns except in very large centralized operations.

The cartel? Anything they can get their hands on really, with a strong preference for the top shelf gear of their opposing army. You can see this in videos of people accidentally encountering cartel members: There's a lot of similarities with normal militaries, but with a few more grenade launchers and heavy machine guns than what one would normally expect.

As an example: I'm an OK machine gunner (or, at least, I used to be decades ago), and while my preferred machine gun (Rheinmetall MG3) is probably not top shelf anymore, I've trained more in tactics with that gun than some cartel member has with whatever fully decked out kit they were given. My job wasn't intimidation. My job wasn't cartel security. My job wasn't keeping track of people straying into our territory. My job was to be the best machine gunner I could be with the hardware that was standardized for my role. And I spent almost all day every day training with that as a premise.

I am of course not saying that I'm better than cartel members but they have other responsibilities too, whereas my focus was on one thing only, and the reast of the squad practiced our roles together extensively.

To approach the subject from a different angle: Let's say you have someone under you, employed to ha dle territorial security- You supply them with the best that your contacts can provide for whatever money you can spare. And in Mexico (which I assume is a reasonable location for your story), this would probably mean an HMG akin to what the US army would use; M249