Ok, so I went with Wood elf, loving it so far, enjoyed the 'tutorial' and the wow exiting the sewers scene, for some reason I then decided to head South East and the town of Bravil, took me an age and then I only managed to get as far as some place called 'Inn of the ill Omen ', really need a horse but I'm guessing they don't come cheap?
Tomorrow I shall continue my journey SE and explore the town of Bravil, it's also weird not having enemies show up as red ticks ala Fallout. eek, the music change freaks me out when an enemy is onto you.
A little bit of advice. I've played Oblivion two different ways: either I fast travelled almost everywhere, or I completely ignored fast travel and just walked (yes walked, not ran

) everywhere. I have to say, doing the latter made me enjoy the game so much more. You miss out on so many cool places and events by fast travelling. So if you happen to have a fair bit of patience, I highly recommend just ignoring the fast travel feature for the most part and just walking or running everywhere. It made the game so much more fun for me.
But of course, it's your game, so above all, just play it how you're most comfortable playing.
As for a horse...the cheapest ones start at 500 dollars for a "Paint horse". Then it goes up to about 1000, 2000, 4000 and I believe there might be one for 4000+, not sure. The Paint horse will do the job for now though. You can make cash the best in this game by going into ruins and looting stuff.
The black horse is the fastest one and goes for 5000 gold. If you want to save some septims, I'd advise against getting a paint horse right away since, being a Wood Elf, your speed will probably be so high pretty soon that you'll be able to move just as fast as the paint horse on your own. If you really want a horse, save up and get one that's a bit more expensive.