I think you will need some basic equipment like: laminar flow hood with UV lamp, CO2 incubator, water bath/thermostat, plate reader, autoclave, plate shaker, centrifuge with changable rotors, set of pipets with dispensable tips, inverted phase microscope (with camera), vortexes and lots of plasticware, and cell culture media with serum, buffers etc. Your lab should be equipped with UV lamps to sterilize air and surfaces.
Another important factor is the staff with understanding of the principles of aseptic work.
Air conditioning is very helpful in the lab but you must remember to have it maintained properly to avoid contaminations.
I hope I didn't forget anything crucial :)
About regulatory requirements ... I think it may depend on your country regulations, but I think that what matters in work with cytostatics is the proper protection of your staff (i.e. laminar hood safety level) and enviroment - how you dispose wastes (never into sewage system), etc.