Stainless or plastic daylight tank, suitable numbers of graduates and storage bottles for chemicals, and a 16x20 developing tray for a tempering bath. Timers and thermometers to suit, of course.
IOW, pretty much the same equipment you'd use for B&W, unless you're expecting to do a SCAD of film.
Unless hot water is free I'd suggest avoiding just using an open tray for tempering. It's easy enough to rig something up using an aquarium heater. Plus it'll be more controlled. Use an old picnic cooler to hold the bath. Insulation is a major plus here.
If you use normal inversion tanks you'll waste chemicals. Considering how much C-41 chemicals can cost it'll quickly add up. My favorite tank for C-41 is the Jobo 2551. It'll do three rolls in 330ml of chemicals. Six rolls in twice that. It needs to be rotated but a motorbase [unicolor etc] will handle that just fine. Use the tempering bath to control your chemicals. Used a 2551 can be pretty cheap. But even paying the high new cost you'll likely save enough on chemicals to quickly pay for the thing.
If you are intending on storing your bleach in a developing tank be certain to store it in a plastic tank. C-41 bleach and 316 SS are not compatible for storage.
A dichromatic colour enlarger for prints, a rotary processor with temperature control like the Jobo for prints and film, and all the other stuff listed above.
I have an Omega C760 and Jobo CPP-2 processor, though I haven't processed colour film (E-6 only) or prints (Cibachromes only) in a long time.