I havn't played in a while and I have no idea what to do in the game, so i'm wondering if I should restart it. I beat the shivering isles and still at the beggining of the story... Is it worth restarting the whole game?

thats up to you

go for it

If it has been a while since you last played it is beneficial to restart, The tutorial dungeon can help refresh your memory on how to play. You can then continue on with an older saved game, or just replay the game with your new character.
Try and use a custom class, read the posts by others on these forums to see what they have done to avoid restartitis. A bad choice in the beginning can make the game very annoying.

I'm starting a new game and naming the character dovahkiin

Are you playing on a PC? Because if so, there are tons of quest mods of high quality that will literally double the length of game.

You can check some of them out http://knol.google.com/k/toql-the-oblivion-quest-list#.

Diversify.

Yes, restart it again.

Sure, I would start you new character. This time, don't worry about doing a list of things; simply let your character live their life and enjoy. Oh, save often and try not to get killed.