That 50$ limit seems to call for some frustration.
I have some serious doubts you can meet that without building the controller by yourself. That seems to include making your own PCB. The PCB is a big cost block even for DIY kits.
Those chinese made controller based on TA8435, TB6560 or A3977 seems to be as cheap as you might get. I remember to have seens them starting as low as ~50$, but transport and customs may have to be accounted for.
The Phidget controller seems to not supported by any controller software like Mach3 or EMC. It comes with C libraries to roll your own system, which seems outside your scope.
The CNC Geeker board is also in eBay for 50$:
But it seems to have two big differences to the chinese ones.
It a) misses any optocouplers to protect your PC and
b) the current is fixed, the idle-current reduction costs extra.
So when you whant to buy a ready made board you will meet a hard limit at around 50$. Even 3 channel DIY kits including PCB might be above.
Staying below 50$ requires you to make the board on your own.
It might even being difficult to get decent components for 3 channels.