Ok, so my mercenary for hire Janessa won't put on any armour I give her. She has none of her own and I can't have her getting killed every 2 seconds so... Any ideas?

I haven't used Janessa, but I know when I use Lydia she can only equip Heavy Armor. Have you tried giving her all types of armor (light/heavy) or is she a mage that can only wear robes?

I'm not sure really. How do I know what kind of combat they prefer?

With the console or the easy way actually giving them two sets and then see which one they prefer.

easiest way seems to be with head slot -> heavy -> light -> hood(cloth for mage) see which she will wear

I give her heavy armour, at the moment shes wearing a full set of Ebony.

Jenassa is a rogue and is very versatile. She prefers light armor, but will wear any armor with a higher damage protection than her current armor. Although you can't check her current armor without console cheats, try giving her better armor until you find some she will equip. Here is some more info: http://elderscrolls.wikia.com/wiki/Jenassa

They don't equip stuff you give them unless it is better than their default. Jenassa will usually equip whatever is the best light armor in her inventory, though sometimes she puts on heavy armor pieces so be careful if you are trying to sneak with her.

I just give her some upgraded leather or better light armor and she's happy to wear it.

Ya I gave Jenassa my Ancient Shrouded Armor and she didn't complain.

Great tips - thanks everyone!

Since I wanted a tank for my mage, I kept giving followers a piece of heavy armor until they put it on. Also, you can use the console command:
getav heavyarmor
getav lightarmor

And see which they are better at.

My Jenessa is decked out in upgraded Elven armor. I never struggled getting her to wear armor.