I've never played a pure mage in any es game but want to try it. Any tips for race/build?

Easiest mage is a breton atronach I find. Make sure they have conjuration as a major skill, dish out the rest of the skills as you want.
When you need magicka summon an ancestral ghost and attack it so it throws spells at you, you then absorb them for magicka. Shrines can also be used for magicka.

Cool thanks. One other question, is the premade mage ok or is it better to make a custom class?

It does the job fine, though you might want conjuration as major instead of minor for the reason above.

Cool, thanks again!

I'm making one after my current character, lmk how it goes

Depends on your opinion about conjuration. I play Breton mage-types almost exclusively but don't take conjuration as a major or minor skill. I know other players think of it as a cool skill, for a non-Dunmer it seems a bit creepy to conjure ghosts, skeletons and zombies - a bit necromantic. That still leaves you with the other conjuration creatures, of course. The most I've used conjuration for has been the summoned armor and weapons. Those are useful and for whatever reason fit in with my char's worldview of what's acceptable for a mage to do.

P.S.: After you play enough, you'll get a feel for what skills you'll like for your char to have. These days I always go the custom route to try variations on a theme

I'm suggesting it for Atronach Birthsign mages. If they don't take Atronach, it's not as good no.
From an RP perspective, it's actually the opposite, Dumner hate necromancy, in other provinces it's considered a legal study (until oblivion).

Speaking of conjuration.... This might be a dumb question but attacking with a conjured weapon still relies on the skill of the weapon type correct?

Correct.

IIRC, the conjured weapons and armor fortify the skill needed to use that item. I don't recall the exact amount, but I think it's either 5 or 10 points while equipped.

If playing a Mage, remember that MANY of the adversaries on Solstheim and Mournhold seem to have Reflect, so each offensive spell you cast is a case of "Russian Roulette". You never know when your "Uber Spell of Uber Destructive Uberness" is going to bounce back and render your character crispy with his or her own magicka. The alternatives are [1] a traditional weapon (in which case, why play a Mage?), [2] conjured critters to do the job for you, or [3] choose spells that you've got resistances or other defenses against, or indirect effects (boosting your own stats, rather than damaging the opponent's).

This is true and for that reason I've found it almost impossible to play a pure mage in the expansions. Usually I develop marksman (or blunt for Sunder) before the end of the MQ and end up playing the rest of the game as a battlemage. It's a bit disappointing but there doesn't seem to be any way around it.

I know that it might be a pain in the a** but you could make some spells to beef up your summons with shield spells and then have heals for them to dish out the damage . It has been a long while since I have played on either of those two sections of the game but I seem to remember it working fairly well. Just a suggestion for a pure mage character is all.

That is how you would have to play it, you're right. The problem for me is not just that it's a PITA, (it is) but also that you become overly dependent on restore magicka potions because you're casting a lot of expensive spells and not absorbing any. Not fun for me at all but it is possible, I guess.

One pitfall I made in my early mages was the assumption that all of my spells had to be a ranged, on target spell.

In fact, spells which are On Touch (as opposed to On Target) can do much more for much less mana, and gives you an excuse to level alteration by casting shield spells on yourself to help survive combat. I might recommend skipping unarmored though and doing at least Light Armor as a major skill and just wear a robe over your armor to retain the 'mage look'.

Also keep in mind that Dunmer are 75% resistant to fire, and Nords have significant resistance to both Frost and Lightning. With my most recent character, ever damage spell I made had a 'frost' and a 'fire' variety. The frost I would use on Dunmer, and the fire I would use on Nords and ghosts/other undead resistant to frost. I've heard good things about the Damage health spell and Absorb Health spells though too, and you may consider those as alternative damage dealers if you don't want to bother making different elemental spells and switching based on what enemy you're facing.

There are ways to avoid using tons of restore magicka potions, the one that I use the most especially since I always play with the Atronach sign with my mage builds is to make a short duration summon of a Ancestral Ghost(~15 seconds) and use that to restore my magicka. The spell I think costs about 6 Magicka and where the first attack from the Ancestral Ghost is always its magic attack it makes it very easy to get the absorbed magicka fast and it is very reliable even at the early levels when you have only the base absorb power from the Atronach sign.
Also, just because you are relying heavily on your summons to deal most of the damage to creatures it doesn't mean that they have to be the only means of dealing with your enemies, you can still throw a couple of spells to aid your summon. When doing this it helps to use spells that you have a significant resistance to or are even immune to as if they do get reflected it won't hurt as much or at all.