I do agree with Wong that a good RUNNING shoe store is the place to go. There really is no simple answer to which shoe is best, as the best shoe is the shoe that fits you while also providing the features you need. There really is a lot of difference in fit and features across brands and styles, so the right shoe is person specific. The only general rules that I think are universal are related to price and wear. You probably need to pay at least $50 (normal retail, not sale price) to get a good quality shoe, and you do not need to pay more than $90. My wear rule is that you should keep track of the amount of mileage you have on your shoes, and replace them every 300-500 miles. Do not wear your running shoes for non-running activities, as the mid-sole will compress (lose cushioning) even while walking.
Do go to a good running store where they video tape you running in different shoes. The only way to really evaluate how well the shoe is working is by slow motion video. You can see pronation and supination without video, but to make an objective assesment of different shoes requires video.
Having said that I will try to address your question a little further. Pain under the ball of the foot (under the first metatarsal head) can be due to several causes, but is most often due to excessive pressure on the first metatarsal head. One cause is over pronation. See my website for a detailed description of pronation and what you might be able to do about it. (Follow the link in the navigation bar titled “Information for Runners Regarding Shoes…”)
Pain under the ball of the foot can also be a shoe fit issue. If your shoes are too long “heel to ball” the ball of the foot will be positioned over part of the shoe that is made to support the arch. Make sure the ball of the foot is positioned in the widest part of the shoe. If you have longer than normal toes, you may need to search around for a shoe that has a long enough toe box to allow you to have room beyond the toes and still let the ball of the foot be in the widest part of the shoe. Again, see my website for more details regarding shoe fit.
Another, but much less common cause, is a “plantar flexed first ray”. This means that the first ray (think first metatarsal and big toe) is naturally positioned to sit lower than the other metatarsals. That positioning means that the first metatarsal head takes excessive pressure. This requires a pad under all other metatarsal heads to allow the pressure to be redistributed.
If the pain is not on the bottom of the first metatarsal head, but in the first metatarsal phalangeal joint (first MPJ – joint between the foot and big toe) then you should see someone regarding the problem. Pain in the first MPJ is can have different causes, and can seriously limit your running future if gone untreated. The common issue is Morton’s toe, which is a short first metatarsal. The problem is that the short first metatarsal prevents the first MPJ from functioning properly. Over time, untreated Morton’s toe can lead to osteo-arthritis of the first MPJ. The solution is a simple pad underneath the first MPJ that effectively lengthens the first metatarsal and restores proper joint function. I am making this explanation so that you know the solution should be simple. However, you should not try to treat this condition on your own. See a doctor.