Its actually a really tough choice for me, all the races are pretty cool. If I really had to choose though, I'd either be Orc, or Dark Elf.
You'd be choosing a pretty hard life. Even within the cosmopolitan culture of Cyrodiil, orcs are looked down on. The only place an orc may really excel is enlisted within the Legion, which welcomes them with open arms.
Orcs in Skyrim are looked down on by the local nords who have invaded and razed the orcish city-state of Orsinium many times over the course of history.
The Dunmer, who have recently lost a huge portion of their homeland to the eruption of the Red Mountain. the rest fell to Argonian invaders from Blackmarsh, many dark elves were lucky if they fled Morrowind with their lives. Their exotic look and culture daedra worship makes life within The Empire often less than ideal. They have no future with The Aldmeri Dominion, who view them and the orcs both as an aberration of the mer form, fit only for slavery and death.
For myself, I would pick a breton, imperial or redguard. I would make my home in The Imperial Heartland. Cyrodiil is beautiful and temperate all year round. The war is distant enough so that things are no longer smouldering, though its mark has definitely been left on the capital and its return surely looms on the horizon.
I'd make my home in Anvil. Warm summer nights, cool ocean breezes and the bustle of a large port city that sees the coming and going of folk from around the world.
For the first time in their history, it is a great time to be an Argonian! As the rest of the world seems to crumble, the lizard-folk have united and grown strong. They are no longer separate tribes; brother fighting brother to sell captives off to the highest bidder. Their former slave-masters, the dunmer flee from their armies. They control now the very farmland in Morrowind they once toiled over in chains.
The so called world powers do not dare encroach on the united Blackmarsh. The region itself would be treacherous for any army to cross, even without the perfectly adapted argonians defending it. Abroad, their lives may not have changed much. They are still reviled and feared, because they are so alien. But within their own boarders they're living like kings for the first time in their history.