I might change it just a little, but not very much.
Federal judges are picked by the president and then are confirmed or rejected by the Senate. This is a good way to do things. This procedure makes sense as the president is democratically elected and so are the senators who vote to confirm appointments. We need some democratic input into the process. However, we would not want to have the judges be elected themselves. This is because judges need to be able to interpret the law without having to think about electoral politics. We do not want judges to be deciding cases based on what decision they think will get them elected to a higher court.
What I would change is the ability of senators to block the appointments without a vote of the full Senate. I would make it mandatory for every appointment to come up for a vote within a specific time frame. That way, a minority of senators could not hold up judicial appointments.