I'm going to make a new mage, probably high elf or breton. I tried playing a mage once before going all out destruction, but even on adept and sometimes apprentice difficulty I kept getting my ass kicked in certain situations because I could kill stuff fast no doutb, but they'd always tear me down faster. I'm not gonna lie, a destruction a mage is who I am, it's what I've played since morrowind, so I will be investing time in and putting points into the tree. But if you all have any suggestions on other schools of magic to invest points in, or atleast learn to incorporate into my playstyle, then I am all ears right now.

Im playing a high elf mage right now and investing in conjuration will be helpful later on personally like the bound swords.
Restoration is a lifesaver for me healing while shooting flames while taking constant damage.
Running out of magic in times of need becomes an issue on more difficult enemies, ive been falling back on one hand and (Block every once in awhile) but i find it necessary whhen playing as mage one hand is invaluable
in combination with enchanting.
to sum up my primary focus is on conjuration, destruction, enchanting, one hand, restoration

If your going to seriously roleplay and stick with it, then a mage on master settings can be quite fun, but you will have to restrict certain spells.

If you don't care, then make a mage, buy frost n flame in riverwood, summon flame atronach in Whiterun and that's pretty much all you'll need. Once that is done take the cart outside Whiterun to the mages college and buy every spell there, congratulations you are now an unkillable magic dealing death machine from hell!