Get a real athletics swimsuit (Speedo, Adidas etc) with a racing back, not a U back. U-backs tend to slip and show a bit more than you may be willing to expose. Also, the slipping interferes with your stroke.
Real swimsuits (not fashion "bathing" suits) are made to withstand chlorine and daily washing and will end up lasting much longer, which is why they tend to cost a little more. Make sure you have 2 suits if you are swimming every day, and rotate them.
One trick I used to do when I was a competetive swimmer was to wear 2 swimsuits when they started to get thin and holey, as did most of the other girls. That looked cute on and extended the life of otherwise unwearable suits.