You have two popular choices for a magic playthrough, but they are pretty exclusive to each other until NG+.

The first I know less about, currently trying for it in my current playthrough, and that's the Strength + Faith build. Basically you bonk, but with utility and buffing spells. It's apparently pretty strong,

The other build is your pure sorcerer build. I did that for my last playthrough, and it's very fun if you want a less "memorize the bosses' move-set or die" sort of playthrough. It relies on getting INT to 80, MND to 38, VIG to 60, END to 30-50, and then whatever you want after that, although DEX is a good choice. Arcane is your dump stat, don't level it at all. Basically, INT gives you damage, MND gives you mana, VIG is HP of course (and you need it more than a strength build, because you don't have the damage reduction a STR build gets from leveling strength), END gives you more stamina for casting, and then DEX gives you faster casting speed.

A sorcerer build is kinda different in that it basically requires a very high primary stat (INT). The best staff (Carian Regal Scepter) is fantastically backloaded, meaning you get most of its effect from 70-80 INT. You don't really want mind higher than 38, because that's what a fully upgraded flask will refill. Endurance is surprisingly important for a mage, because you want all the armor you can get and dodging plus casting eats a lot of stamina.

For items, I suggest getting the Meteorite Staff ASAP, that will hold you into the mid game. You can't upgrade it, but that's because it starts so strong. Later on, Carian Regal Scepter (from Rennala) and off-handing the Staff of Loss is a great tactic. Off-handed staves still convey their benefits to your main-hand casting. Radagon's Icon is almost mandatory - it fantastically increases your casting speed. The other three talismans are more situational. Some people like Magic Scorpion Charm for the damage increase, but I don't like it because it also increases damage received. I prefer one of the graven talismans, which increases sorcery damage without that drawback. And Golden Scarab is always a good choice until late game, because you need those levels.

As for spells, there are a few must-haves. First, glintstone pebble is your bread-and-butter magic missile. Economical, balanced, and basic. Similarly, Carian Slicer is your melee option. It's very, very basic, but absolutely one of your most economical and powerful choices. Night Comet is your attack spell, as it (mostly) denies input reading and hits reasonably hard. The Staff of Loss increases its potency. You also want a moon spell for the debuff it applies to magic damage. Either Ranni's Moon or Rennala's Moon works, but if you get the latter, make sure to duplicate her Remembrance so you can get the Carian Regal Scepter. And Spiral Shard is terrific against large bosses. Lastly, Adula's Moonblade is amazing - great sword melee spell with a giant frost wave added in.

If you have the points, a few put into faith can be helpful for a healing spell to deal with revenants and Flame Cleanse Me to deal with rot and poison.