Always go standard with MAUs unless you are desperate to end a stalemate with a ship with shields.
Other weapons are useful in PvP, as they attack before marines and can do bonus damage in the case of lasers vs shields and railguns vs armor.
Of course you can always use regular weapons in COM missions if you want
they just aren't as efficient
Basically all of that. I'm far from a vet in terms of this games combat but having learned a fair bit from my experiences as well as from folks like Raphel, Dadds and Jam I have learned enough to do pretty well for myself.
If you are just starting out then like Rostin said, you just want to use Marines and Shields on your ships, for the reasons previously stated they can attack multiple targets multiple times and they do not miss. Normal weapons such as Vipers, Lasers and Railguns aren't that effective for COM missions because #1 they can and often do miss #2 because most of the time your ship is out numbered and you only have so many shots with those weapons and #3 because the Marine/Shield combo is also pretty much a tank build as the Marines are not only offensive but provide defensive HP as well.
Like Jam I prefer to have some weapons on my COM ships just in case I need to use it for something else and it cuts down time when you want to shift gears from COM's to PvP.
As far as the odds are concerned, whether you win or lose is often determined by a few things. The obvious is how many opponents you have to fight and how strong they are compared to your ship. The not so obvious is what kind of ratios you have on your ships as far as how much of your total power is made up of shields and weapons and then how much of your weapon power is made up of Marines and Firing type weapons. A fairly standard ship build that a lot of folks know is making sure that half of your total ship power is made up of your shields. That results in almost any COM mission that ship could pick up having less total power than your ship has shields most of the time as Rostin mentioned earlier.
You will have to play around with some different setups to figure out what works in which situation. As far as Marines and COM's are concerned I have this advice for you. You should split up your Marine power between 8-16 different Marine Modules. The reason for that is two fold #1 You don't want to put all your eggs in one basket and just put one super powered module in there as Marines now fatigue after each attack so their power will go down with every attack against any enemy ship/station/planetary force. #2 You don't want to spread out your Marine power too much otherwise you require too many attacks with your Marines to take out the enemy and they may get through your shields and start depleting your Marines which might seem cheap to replace at first but when you start needing to replace tens of thousands of them after every battle it quickly gets expensive.
Do keep in mind that is my general load out which also includes 8-14 Vipers depending on what lvl modules I'm working with to hit my power ratios for my ship layout. If you go with full Marine research and load out for your offense then you may require more or less depending on the levels of your tech.
However with my standard load out I have won a battle with 7:16 odds in the enemies favor (which only happened because somebody dropped a COM mission on top of mine, otherwise getting odds like that is pretty much impossible unless you lay down multiple COM's at the same time in the same place of the same type). Others have won battles with far worse odds using things like the Death Rays and other hard to acquire tech.
Anywho that is just my two cents, take it for what you will. You might not want to use my setup but I hope it can at least give you some ideas as to what you may or may not want to do.