While the best type of shoe depends on the foot issue in question, anyone should choose shoes that fit the feet well without any tightness. People with problem feet should avoid shoes with narrow toe boxes or high heels.
Shoes that properly fit the feet not only relieve foot pain, they also help prevent foot issues. As such, it's important to have a professional measure the feet regularly. From there, select shoes that conform both to the length and width structure indicated by the sizing.
A main cause of foot problems, such as bunions and plantar fasciitis, is shoes that constrict the toes or offer inadequate support. Choose shoes with good arch support and cushioning around the heel and ball of the foot. Likewise, people with bunions need to select shoes with toe boxes that don't constrict or rub on the widest part of the foot.
Supportive shoes should also be rigid, but not inflexible. The shoe needs to bend at the toes, but not collapse on itself. Likewise, the part of the shoe that wraps around the heel bone should be firm when squeezed.
In general, high heels, flip flops and ballet flats exacerbate foot problems. High heels are the worst as they encourage the formation of bunions, aggravate plantar fasciitis and achilles tendonitis, and cause pain in the ball of the foot. Flip flops and ballet flats don't offer enough support for people with problem feet.