WingedKagouti: If going with the premade classes only and with a focus on Enchant, a Breton Sorcerer born under The Lady seems like the primary pick. You'll have a slightly larger than average pool of Magicka for spells, but Bretons are also decent with weapons. Sorcerers having Heavy & Medium Armor as Minor Skills mean that they have a natural inclination towards the Armor pieces that have the best Enchant capacity. The Lady will provide you with more starting Health and make people less hateful towards you.
Alternatives would be Altmer, Witchhunter and/or The Mage. Altmer and The Mage are for a more spell focused path and both do work well with Sorcerer. Compared to Sorcerer, Witchhunter emphasizes weapon skills a bit more and also uses Light Armor instead of Medium/Heavy.
A few thoughts on this:
Altmer and Breton suffer from having low Strength. Given that the items capable of the best enchantments can get pretty heavy (Daedric Tower Shields, in particular, have 45 weight), this can be a problem.
Heavy Armor is a decent option due to such items being nicely enchantable. On the other hand, the Boots of Blinding Speed (which are quite useful) are considered Light Armor.
I will likely be using a custom class, with Enchant as a major skill. I am thinking that Restoration and Conjuration might be good to have; Restoration to fortify stats and skills (especially since the same stat/skill can be fortified multiple times in one spell, and doing so gets expensive quickly with enchantments but not spells), and Conjuration to summon creatures to trap their souls (in particular, Summon Golden Saint might not be easy to fit on an item that isn't too heavy). Maybe Mysticism as minor?
Race-wise, I actually think Orc might be a good choice; good starting Strength and Endurance, while Intelligence (for females) and Willpower aren't that bad. On the other hand, I don't get any Enchant bonus with this race (and Enchant levels up very slowly).
I was actually thinking Atronach for the birthsign; the spell absorption and extra Magicka are nice for when I need it, and Stunted Magicka is mitigated by the fact that item charges recover on their own. Also, summoning Ancestor Ghosts and turning them hostile can allow Magicka to recover in the wilderness.
I am thinking that Strength (for carrying capacity) and Endurance (for HP) are the stats to focus on at first. Should my class use those stats, or should I replace Strength with Luck? (Endurance is important because, unless I decide to use the Code Patch or do silly exploits with Drain Stat + Fortify Fatigue, you really can't use magic to fix low Health.)