but I'm largely randomly selecting that stuff with no real understanding of what I am doing and it seems to make no difference - any mission it suggests I've been able to complete with no problems. So I'm not sure why that makes a difference?
It won't make much of a difference until you start utilising your chosen role.
Right now, while you're getting from 1-30 in the solo missions, you pretty much only need to concentrate on the standard DPS role - kill everything as quick as possible to get through, but the game allows you to take on your Tank, Controller, or Healer role once you hit lvl10. You can play around with that role at any point past 10 (push up on the d-pad and select 'switch role'), but it isn't recommended to use that role exclusively until you hit 30. The roles break down like this...
DPS - what everyone starts with. Your job is to inflict as much damage as possible, and you don't need any kind of support abilities. You want to focus on increasing Health, Defense and Might stats.
Tank - You are the target. It's your job to get the attention of the enemies and keep it so the other group members can attack or do their job without getting overwhelmed. You want to focus on increasing Health, Defense and Dominance stats. Also can't hurt to get your Restoration as high as possible if you're a Fire Tank.
Healer - Speaks for itself. Concentrate on increasing Health, Defense and Restoration.
Controller - Provides power restoration to allies, and restrict the abilities of enemies, such as reducing their ability to heal or damage. Concentrate on Health, Defense and Vitalization.
You'll notice that some of your powers will say in the description what they do in a support role as well as a damage one. Some of those powers interact when used together to give you added effects. It doesn't outright tell you all that because it wants you to play around and find out what works best for you and your playing style, rather than everyone cut and pasting the same powerset.