The first consideration in choosing a martial art is finding which schools are readily available to you in your area since you will be spending a lot of your time traveling to and from the school. Then visit each nearby school, increasing the travel range until you reach the limit of your comfortable driving range.
The next consideration is the style or styles being taught at the each school. Judo and Taekwondo are Olympic sports so they are sport oriented. Judo has lot of physical contact, similar to that of wrestling, so it is very physically demanding. Taekwondo's level of contact depends on whether it is traditional (light-contact) or sport (heavy-contact). Karate and Kung-fu styles are usually light-contact. Full-contact styles require a unique personality since there is a higher chance of injury. Injuries are not just painful or possibly dangerous; they also prevent you from training while they heal.
Judo has throws, pins, chokes, and arm bars so there is much hands-on contact. Taekwondo specializes in kicks. Most Karate and Kung-fu styles specialize in hand techniques. Taekwondo and most karate styles are hard styles in that they use bone-to-bone blocks and linear attacks. Kung-fu styles and some Karate styles are soft styles that use defecting blocks and circular attacks. Hard styles are more suitable to powerful, less graceful people. Soft styles are more suitable to graceful people who can move quickly. Weapons are something to learn after you become proficient at empty hand techniques. They compliment empty hand techniques, not replace them. There may not be any weapons available but you always have your hands and feet with you.