Bob, not to belabor the obvious but the minimum requirement is that it can be attached to your lens of choice's filter threads. Your T3 doesn't control flash through the lens so TTL-auto is irrelevant. Self-quenching flashes don't know about compensation for magnification, so aren't easily used for closeup work.
Coupla not too obvious considerations. Here's an exercise that will illuminate them: Choose the film speed you want to use. Choose the range of magnifications you're going to work at. Calculate flash-to-subject distance for the lens of choice and a couple or three (lowest, highest, middle) of the magnifications you expect to use. If you don't know exactly where the ringflash will sit, assume that it will be 1" in front of the end of the lens' barrel and 1" outside it. Decide the effective aperture(s) at which you want to work. Then use GN arithmetic to determine what GN the flash has to have to give good exposure at those apertures. Finally, calculate the worst-case (high noon, no shade) effective aperture wanted with your desired film speed and your T3's top sync speed (1/125, isn't it?). With ISO 100 film, effective f/16 or so. At 1:1, that's f/8 set. Contemplate what diffraction will do, then ask whether you wouldn't be better off with a camera that syncs flash at a higher speed and curse EKCo for discontinuing KM. Also do some searching to find the GNs of ring flashes you're likely to encounter. Use GN arithmetic to find the effective apertures they imply at your intended magnifications with your film of choice. Curse again.
One of my solutions to this little headache is an FM2N or N8008S (sync speed 1/250) and a Spiratone Macrodapter with two little flashes and ND gels as needed on the flashes. The Macrodapter has been called the poor man's ring light; it holds two little flashes alongside of and a little in front of the lens. The Macrodapter has one advantage over ring lights; it gives better modeling while a ring light gives rather flat illumination.
The other is to use a 2x3 Graphic with a Copal #1 shutter (sync speed 1/400) and a variety of approaches to lighting. Just got another Macrodapter to try on it this spring, if it comes. There's also a Jones of Hollywood bracket that's functionally equivalent, in some ways a little nicer.
Sorry, I'm a modeler. And you need a model to decide what you can get away with ...