So I have never actually played as a full mage before and I am looking for insight on how to do it. I know that Altmer are the best to do because of the high starting stats but I am not very good at pairing magics together (or they level unevenly). Just looking to see how other mages play to kind of mix and match for my own niche style of mage!

Friendly word of advice. The mods don't like it when you create multiple threads in different forums on the same topic.

Conjuration plus illusion is pretty useful and fun to mix and match some good combos with.
Destruction is good at lower levels but becomes boring and limited as you level up.

I tend to run a lot of mages. My recommendations are that you pick your schools carefully and plan ahead. Magic in the base game scales poorly so you want to max out your skills while staying low enough level that you don't get bored or try to finish fights with gimmicky behavior. If you are on PC I suggest a minimalist mod like "Better Magic" to make your mage happier.

Altmer aka High Elves are good for the starting mage. They have excellent +magicka and the highborn ability allows you to compensate for the poor magicka regen in the game. It is great vs dragons or tough fights.

I personally don't love Conjuration though it is fine on difficulty levels other than Master+. I think a good first mage set is Destruction/Alteration/Illusion with a side of Resto. Consider Enchanting if you want to make your own gear and use the fortify enchants. They are the path to lower cost. Magicka regen is a trap except for the highborn ability. It is almost always better to get fortify on gear rather then a buff to magicka regen.

Do not neglect Alteration since you need the defense and it helps with mage fights too via Magic Resistance and Absorption. Do the Book of Love quest too. The Lord Stone is a good choice. If you chose illusion focus on bandits and human targets early on so you can get used to using it and get it leveled up. Don't neglect your shouts. You get "Become Ethereal" early on and it is great for mages.