If you need a particular weapon, like a Shotgun, Assault Rifle, Battle Rifle etc, you can swap your current weapon with a marine to take his. So marines can be a good way to get weapons in certain situations.
Additionally, a marine will carry any weapon you give him until he is killed, or you swap with him again. This also means that marines can be used to transport weapons. Say you know that you're going to want a Sniper Rifle you've found later on in a level, but you don't want to carry it with you in between. If you give it to a marine, you can carry two other weapons, and then simply swap with the marine again once decide you need the Sniper Rifle, provided that the marine has survived to that point in the mission.
An element of this that can be used to even greater advantage, is that marines don't use any ammunition. What this means, is that even if the weapon you give to one only has one round of ammunition left in it, the marine will be able to use it without limit. This also means that while transporting a weapon for you, the marine is free to use it without expending any of your ammunition.
Important to note here is that you can't give a marine an empty weapon.
In short, if you've got a decent weapon that's almost out of ammunition, give it to a marine; while the marines may not be able to operate weaponry as effectively as most players, you will still likely benefit more from having the desired weapon as an asset to your mission in the hands of a marine than you would if you had depleted it yourself and thrown it away.
They can also be used to refill ammunition on a weapon that both you and a marine are carrying. As long as you have at least 2 extra (and unique) weapons nearby, you can swap your low-ammo weapon for one of them, then swap it to the marine for his weapon. At this point, you should be holding the marine's weapon, and you need to switch it for the second unwanted weapon, making sure that you drop it at least a few meters away from your original weapon (if you don't want to collect its ammo and completely deplete it). Then pick up your original, low-ammo weapon again (dropping the second unwanted weapon) and give it to the marine, then finally switch the first unwanted weapon for the higher-ammo one you left on the ground.
This process is actually much simpler than it sounds, and you should be able to figure it out easily on your own while playing.
Because of the fact that marines don't use ammunition, I always try to give my marines certain weapons once I've almost depleted them (particularly explosives). In order starting with most desirable:
- Fuel Rod Gun/Cannon
- Rocket Launcher
- Brute Shot
- Sniper Rifle
- Beam Rifle
Depending on the circumstance, you may want to give your marines different weaponry, but to be brutally honest, I almost never really notice their "support" unless they're equipped with one of the above weapons.
In regards to the Warthog, I also often try to make sure that the marine in the passenger seat is equipped with a Rocket Launcher or Fuel Rod Gun/Cannon. This seems to be easily the most effective strategy in most situations. However, in rare circumstances you may want to equip your passenger with a weapon that can be fired more accurately, or rapidly.