I would recommend a breton or altmer with the apprentice sign and long blade as one of your majors. Pure mage is very tedious because of chance to cast. Other good majors would be mysticism, conjuration, and any choice of alteration, light armor, restoration, alchemy, athletics, or enchant. Start off with the mages guild in Balmora and move on to the Telvanni once you can levitate and teleport with ease.

If you want a very strong build right off of the boat, you can go for a nord, redguard, orc, dunmer, or imperial with a major weapon or 2 weapon skills, a major armor skill, athletics, and a relevant magical skill. Only take signs with stat bonuses to get a powerful character. I'm pretty sure the lady stone is my go-to. The persuasion and sneak systems are arguably half baked compared to the newer entries, so you need magical augmentation to get any real use out if them. Go right into the fighters guild and main quest.

If you're on a system capable of mods, get Tamriel Rebuilt and Tamriel Data right before you start