First, here's my top card for approx $100USD budget (after rebates)->
http://pcpartpicker.com/part/evga-video-card-02gp43751kr
- for a bit more I prefer this card (Asus Strix)->
http://pcpartpicker.com/part/asus-video-card-strixgtx750tioc2gd5
How bad are the GT610 etc?
The following benchmark averages a lot of game AND is done with a good CPU to minimize bottlenecks there (so weaker CPU's will get lower performance). It's still quite useful though:
https://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_750_Ti/25.html
1) GTX750Ti is about 3X more powerful than a GT640, and
2) GT640 vs GT610-> 384 cores vs 48 cores, 4X texures/ROPS diff
Again, this doesn't scale perfectly but you can still see how vastly different these cards are. It's too involved to go deeper into this, though if I had to guess then the difference between the GT610 and GTX750Ti in terms of FPS might be somewhere between 5X and 8X real world difference?
Like say 10FPS vs 60FPS for the same game?
Other:
NVidia is usually recommended for weaker CPU's since the AMD DX11 drivers use more CPU cycles thus more prone to bottleneck.
Other:
PSU-> GTX750Ti can get by with a quality 300W usually. In some cases less depending on rest of system. The one I linked uses under 75W, so if you only used 150W max for the rest of the system you're still at 225W or 75% PSU load.
Other:
Below a GTX750Ti the value diminishes rapidly. For example, if you pay $100 for a 750Ti, then $50 for a GPU will get you wel under half the performance.
Other:
32-bit Windows?
If so, I recommend a 1GB video card. Otherwise get a 2GB video card. (You can upgrade from 32-bit W7 or 32-bit W8.1 to W10 64-bit for free though)
EBay/used?
Warranty issues, but if really stuck at least look up benchmarks.
Games you want to play?
Rest of your system matters too, but it's hard to recommend anything much weaker than a GTX750Ti.