Generally speaking, fighter pilots don’t choose their aircraft. Like most aspects of the military, fully trained fighter pilots are required to fly whatever they are told to fly. The aircraft is usually distributed depending on strengths and weaknesses, such as whether someone is a better team player than others. Some team players may be asked to lead the crew, where others may benefit from solo flying with fast jets.
After completing the training, pilots are often asked to submit their preference of which aircraft they would like to be assigned. There is a ranking system amongst new recruits that will also determine who gets what aircraft they want. Those in the top ranks will usually get their first pick, but only from the aircraft available at the time.
The short answer is that it depends, but for the most part, fighter pilots don’t tend to choose their aircraft. They can submit their preferred aircraft in hopes to be assigned to, but it comes down to the military branch. They will choose who gets to fly what aircraft depending on their ranking system, skills, and weaknesses.