Anybody got a good way of level up destruction? For example, is it better to use fire or firebolt?

Well, just use it a lot, it will lvl up for itself. I made an imperial warrior, I never tried to boost my one-handed skill, I just use it in every situation and right now I got 93!

Use higher level spells to gain levels quicker. I personally am a big fan of using fireball on every peice of wildlife i come across. Particularly foxes and rabbits. Damn rabbits come in here, eating my grass....

Flames + healing hands on your horse.

Generally speaking, if you focus on Destruction as a means of doing damge it will outpace your player level and thus enemy scaling as well.

I just used every Destruction spell I could as I got them. Flames, Sparks, Frost, Runes. If you want to start slowly, you can go near Mudcrabs, they'll attack you...they can kill you too; they're stronger now. It'll level pretty quickly.