Yes, you can use a bench grinder. You will need to remove the guards and mount it to the edge of the bench (or a stand-alone pedestal) for best access.
Any bench grinder could work. If you don't already have one, even the cheapies at a place like Harbor Freight would work. This assumes you're not investing in the tool for actual grinding purposes; if you need a good bench grinder, then get a good bench grinder.
If you're wanting something specifically for buffing, but can't afford a "true" buffing machine, a bench mandrel may serve the purpose better than a bench grinder.
The issue is shaft length. On a converted bench grinder, you're limited on the approachable angles because the motor gets in the way unless you use the larger-diameter wheels. A mandrel would allow more access because the motor isn't in the way.
You asked about speeds.
It really depends on the material you're buffing. I like to use higher speeds whenever possible in order to get the job done quicker. But some materials won't tolerate high speed. Fortunately, most of the materials we use in knifemaking allow some overlap in speed selection. That allows us to keep the same speed for a variety of materials, meaning you're not constantly switching to a different wheel diameter.
Here is a range of speeds that seem to have provided the best results for me.
The reason there is a "range" is because not everyone applies the same pressure, and not everyone uses the same compound.
Since these are not exact, don't go overboard trying to obtain an exact speed. Just try to get in the general window of what has been proven to work well.
All speeds below are surface speeds (SFPM).
Stainless steel...................... 3500-5000
Steel.................................. 3500-7500
Copper, brass, etc.................3000-7000
Aluminum............................. 3500-7500
Titanium.............................. 1000-2500
Wood, plastics, finishes, etc... 1000-2500
Remember, these are surface speeds, not RPM.
So if you're using a wheel running at the same RPM as the motor (the case with your direct drive setup), you change the wheel diameter to change SFPM.
The typical bench grinder will have a motor speed of approximately 3450 RPM. So let's see what surface speeds you're gonna get by mounting different diameters of buffing wheels to it.
4" wheel....3613 SFPM
6" wheel....5419 SFPM
8" wheel....7226 SFPM
So you mentioned that you prefer 4" or 6" wheels. Coupling that to the typical bench grinder, you're covered for the metals. But you can't get in the window for best speeds on the handle materials, titanium bolsters, etc.
Many people have asked questions on why they can't get their Micarta, G-10, etc. to "look right". And there will be all sorts of answers. But I maintain the fact that most of us try to use a "universal" speed for the entire knife, when we would be better served using different speeds. Not the answer everyone wants for production, but it's the only answer for quality.
So that's why the motors on many of the "professional" buffing machines you look at have the lower speeds (1100 RPM is common).
The lower motor speed gives you increased flexibility regarding wheel size- it allows you to get those lower surface speeds without resorting to using a miniature wheel in a rotary tool.
But, as you've noticed, budget is always a concern. This is another reason why a mandrel may ultimately be better for you than a bench grinder. A 1725/1750/1800 RPM motor can then be used. Or even if you still use a 3400-3500 RPM motor, you can still use pulley reduction since the bench mandrel is not a direct drive setup.
As with everything else, the type of setup you use will be heavily influenced by the needs of your particular projects.
A person doing small items may not need the same access as a person doing larger stuff.
Likewise, some people don't delve too deeply into what's required for the "ultimate finish", so working within the optimum speed range isn't important to them. They simply say "it's buffed", and call it a day.
Only you can know what level of finish is needed for your work.
Good Luck,
Rob