PDA may have similar problem as PSP when reading on a small, back-lit screen. But, I bought a used Blackberry 8700C for $40 and installed the MobiPocket reader on it. It's good for "stealth" reading or when it's inconvenient to pull out my Kindle. The best experience is going to come from an eBook reader with an eInk screen, but none of those are available for the price you say you can pay.
The
eBookwise EB-1150 costs about $100, which is more than your budget, but may be a reasonable alternative for a while.
Good luck.