If you plan to do advance training with your dog, make sure that you give yourself enough time for training, and that your dog will still be physically able to accomplish your goals. Physical soundness is a major concern, especially if you plan to do advance training. Fiddle fronts, knuckling over, and weak rears are just some of the problems that can affect a dog's performance. Some people try to compensate fro an unsound animal and tend to keep their dogs on a light side weight wise to minimize the stress and trauma caused by jumping. Although you should never jump an overweight basset, there is a big difference between good weight and under weight.
Mental soundness is also very important.
Personality and temperament is a major influence on your choice of training partner. Adults tend to be easier to peg than a puppy in respect to what temperament they have, but extreme personalities are visible at any age. Remember, you want to also be able to live with your basset. You want a dog that will be a buddy as well as a competitor. Recently, our breed has been getting some bad press regarding their assumed lack of intelligence.