As John said already, the most important part is the device support.
Manufacturers of various EPROM programmers will typically publish long
lists of devices that their programmer is designed to support. First
make sure that the devices (EPROMs) you need to read are supported by
the programmer you intend to buy. Often commonly available "popular"
devices were made by multiple manufacturers and were known by various
similar names, so when looking up device types in a list, it may make
sense to look up the other known compatible type names too. However
beware that there are some devices by certain manufacturers that are
known to be "quirky" and that some theoretically "compatible" devices
need not always be fully compatible. In the most cases a "compatible"
device will at least be compatible enough to read identically, but when
it comes to programming them, beware - there be dragons in the details.
As for any particular programmer, I can't really recommend much due to
the lack of experience. I've used a MiniPro TL866A in the recent past
and found it to be built and working reasonably well. However, I only
had recently made serial EEPROMs and Flash-PROMs to program, nothing
from before the 2000s, let alone 1980s, so no experience with them.
Anyway, here is the device support list of the MiniPro TL866A:
http://www.autoelectric.cn/minipro/MiniProSupportList.txt
Note that some of these devices are micro controllers (AVR, PIC) with
serial interfaces, for these the TL866A (but not the similar TL866CS)
has an in-circuit serial programming interface available via a second
port. Apart for it (the ICSP) these 2 programmers operate identically.
Dimitrij