There are no birthsigns in Daggerfall. Instead of that silly system, if you choose a custom class you get to choose up to seven advantages and seven disadvantages for your character. The more advantages you take, the more difficult it is to advance your skills, and the more disadvantages you take, the easier it will be to advance your skills. You can create a ridiculously overpowered character who will have a difficult time leveling up, or a severely crippled character who gains levels quickly, and everything in between. A much nicer way of doing things, if you ask me. You can also kind of exploit the system by giving yourself disadvantages that don't really hurt your character very much and then taking advantages that significantly lower the difficulty of the game, but I wouldn't advise this as the game is really most fun when you create a character that will provide some sort of challenge to play.
As for what type of character to play, that's really entirely up to personal preference. The first time I played the game, I chose one of the pre-made classes and beat the game as a Breton healer. The second time I went through the game with an Argonian custom-class assassin type character with some skill in the magic schools of illusion and destruction. Really, there is no wrong way to create a character, unless you create a character with no combat skills whatsoever who also has phobias of every type of creature and critical weakness to paralyzing...that might make the game a little
too difficult...but other than that, play whatever type of character you would like to play as. I can assure you that both the spellsword and the thief/assassin will be enjoyable characters to play. If you ever decide to make a custom class pure mage character, though, I really advise that you choose 3x increased magery as one of your advantages.