Well, it's hard for me to answer this without knowing your script or storyboard, but the simple answer is very carefully. If you can avoid actually hanging the actor, or doing a long shot, that would be massively advisable. If it were me, I'd have the actor 'hung' but standing on something, shoot from the chest or naval up, and have him writhe around and act it out that way. DO NOT, under any circumstances, actually hang the actor, even for a short time. That sort of thing requires a stuntman, a stunt co-ordinator and a budget.
As for prop costs... You need a length of rope. If you know where to look (boatyards and farms are good, as are scouting groups) you can probably borrow/get one for free.