Rule #1 of skyrim: Do w/e the frack you want

You want to be a magic wielder high elf who hacks enemies in half with a 2hander?... go for it.
1 thing you might want to be aware of is that in end game, magic damage stops scaling (it caps out) whereas melee and archery keep going past ridiculous levels. It's not that magic dmg doesn't go high enough, it does.... it's more that the weapons allow you to get even more powerful. They don't have a damage cap. Still magic IS fun, and you CAN play and beat the game using it (I wouldn't recommend master difficulty though

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I'll drop some magic wielding advice though...
forget daggers/shields. You can have spells in both hands. Most of the time it will probably be 2x whatever destro spell you're using. You can double your DPS by doubling up your flames... makes sense right?
Magicka regen is slowed in combat (as is health and stam regen) and you only regen magicka while NOT casting (or holding spell ready to cast) So you need to get used to managing your magicka. cast for a bit, then rest and dodge for a bit while it regens. This pretty much will be your play-style throughtout your mage career. You will find staves over time giving you something you can do while allowing your magicka to regen as you progress... but early on it's just cast and run... cast and run.
You know how you can 2x flames to double dmg output? Well you can 2x heal to double your healing rate too. This can be critical.. ESPECIALLY with the first tier healing spell.
You'll want to take perks in Restoration, Destruction, and Conjuration. You have a choice of either wearing armor or using Alteration for your defenses. You might find light armor as a better choice as a new player since it requires a LOT less management on your end. Alteration on the other hand gets some bonuses in the form of magic resistance and paralyze, but you really don't NEED these. You might even decide to go with heavy armor for maximum physical damage reduction... but you can hit the armor cap with light armor anyways.... and you might like the look of Elven or Glass on your mage (their lighter and flashier). Alteration is the "Pure mage" way to go, but generally considered more challenging. (until you max it and start absorbing magicka from enemy spells O.o ) Alteration also takes up a fair # more perk points (though they are good perks)
Conjuration is your summons.... you'll want to summon pretty much ever fight if for no other reason than to advance your conjuring skill. Summons are really one of your primary forms of both damage and protection all wrapped up into 1. It's not very "active" though (you cast and then do nothing) so you back it up with your own destro
Illusion can be fun... but undead and mechanical enemies are immune, and it also has level cap on every spell and the school is pretty useless unless you fully perk it out. Illusion is more suited to thief/assassin types IMO but you can fully spec into it if you really enjoy it. There is some fun to be had, but IMO you're best off with your core 3 schools.
I also recommend Enchanting as your crafting skill. You'll want to be recharging staves anyways, and enchanting gear will help you make some pretty epic and useful gear later on.... including a set of alchemist gear allowing you to create better potions without even perking for em!