Yes, you need a new PSU and case. As shown in your other thread, your case is non-standard BTX.
A series (A320) boards do cost less, however, they do not have support for newer Ryzen CPUs, limiting your upgrades in the future. Also, A320 boards have fewer BIOS updates and tend to have worse memory compatibility. Also, A320 boards cannot overclock your CPU.
B350 and B450 boards eliminate all of these issues. B450 should have better support for upcoming CPUs.