Several attributes make Biblo Baggins a good thief, both mental and physical. Although Bilbo initially does not realize that he is the ideal thief, Gandalf spots his potential quite early.
The first attribute is that hobbits are short, making it easy for them to fit into small spaces. Next, they can move very quietly. Biblo also has excellent manual dexterity, and agility enabling him to pick pockets as well as doing magic tricks. He also has very acute vision and decent night vision.
The main qualities, though, which qualify him for the role have to do with his mind and character. First, he is honest, loyal, and trustworthy, all rather unusual characteristics in a thief but needed in this case. Next, he is very patient and articulate, able to get himself out of trouble by negotiation. Something that becomes important by the end of the book is his ability to use the Ring without being corrupted by it.