I personally think Feste would be the most interesting character. He is someone that we actually know very little about, but he is unique in being part of both households (Olivia and Orsino's households) and also, although he apparently plays the fool, he is given speeches that show his incredible insights into situations. It appears that he is a character that knows and is aware of far more than he lets on. He also gets to sing a lot and be a fool whilst given the last, oddly melancholy song at the end of the play.
I saw Twelfth Night for the first time at about the age of twelve and I still remember Sir Toby Belch; I would choose to play him simply because he's the most colorful and memorable character (for me) in the play. Although I do not drink, I also think that as an actor it would be a challenge to portray a drunk without totally typing the character. I think character preference largely depends on the actor's personality. I enjoy playing the "over-the-top" character, the character who gets much of the audience's attention. The role of Sir Toby is perfect for the actor who enjoys "hamming it up" or perhaps overacting. :)
I think Olivia in Twelfth Night by William Shakespeare would be the most interesting female part as she is the focal point of all the attention in many ways - so for an actress who likes to play beautiful roles,wear pretty luxurious costumes and be flattered and pampered - this is the part for them! It would be interesting to research historically too - the manners, customs and etiquette of courtly behavior of the day - and fun to act all prim and proper and correct. She is also quite kind so it would be nice to know you're playing a good character.(She puts up with Sir Toby's funny ways and she tries to be inclusive towards Malvolio in the festivities near the end.) She would be interesting too for her flightiness and mood swings and the way she switches from one person to another.