Sorry,
midgetgreen11, the only answers we allow to this type of question are: Consult a Qualified Rigger; and Consult the Projector's Manufacturer. There is NO "safe and economical" method. Some may be less expensive than others, but this falls squarely under "if you have to ask, don't do it."
As to "how well will it work on a
cyc?", set the projector up on a roll cart on the stage floor the same distance as the intended
electric, and point it at the cyc. Image quality depends on the quality of the projector, the
lumen output of the projector, the intensity of the surrounding stage lighting, and other unknown variables.