I've played as a mage once before, mainly using Destruction, Conjuration and Restoration, but it didn't work out too well, as even into my mid 20's, I was still having trouble against basic enemies like bandits and animals.

So I'd like some advice on building a good, fun and powerful mage. I'm considering making Illusion my main magic school; what would be the best combination of schools to use with this?

I have Googled different class set-ups already, but I'd just like to get the opinions and experience of my fellow forum goers

Illusion and Conjuration is the most powerful, and even considered to be overpowered, school of magic duo in the game. A careful strategy will grant the player the ability to advance the entire game and never take the first hit of damage. The only thing that may hit you are the occasional trap. Namely the swinging axes in hallways.

I agree. These are the two most powerful schools and in conjunction with each other they clean house. However, until you get illusion to 90, and take the perk, it won't affect undead. It can also be tricky to use illusion sometimes, since you can only get enemies fighting each other if they are closer t each other than you while the spell is in effect. Hitting them from sneak works best, or hitting them from a distance.

If you can give more detail about what your problem was and what you are trying to achieve with the build, we might be able to give you more specific advice. There are all sorts of theories about how to build a good mage. None of them are "wrong" per se, but some are stronger than others and they go about things in different ways with different results. Like, do you boost magicka regen with your enchants just going for cost reduction enchants. Cost reduction enchants are more powerful, but boosting regen speed can be more fun if you like to manage a magicka pool. In general, I forego the perks that reduce casting cost and use enchants (either in game or self made) to manage my casting cost.