I recently got a new smartphone, i wanted a really good one for less than 300 euros, new, no contract, for use with prepaid. That may be too pricey for you.
Anyway, i settled for a samsung galaxy S5. Its really good, really fast, and you can easily replace the batteries and the display. So you can buy a used one, where the batteries have gone weak or the display is broken, and fix it yourself. Maybe you can also find a new one for below 300 dollars.
I think its worth it because its a really good phone that can last many many years.