We used a toddler bed for quite a while. My daughter got too tall for it but always sleeps curled up anyway so she still loved it. You certainly can look second-hand but do be very careful about condition and be sure to check carefully at www.cpsc.gov (Consumer Product Safety Commission) to see whether whatever you get has been recalled. You can search on the site for past and current recalls. Or you can go with a twin bed with bed rails - the online catalog One Step Ahead sells several kinds of bed rails and you can remove them and take them on trips etc. if needed.
I know a lot of families want kids to stay in cribs as long as possible, but at 3 he probably is able to climb out. If they are tall enough to climb out, whether they've started to do it or not, I think it's time to move them out for safety. What influences me is that a friend's child broke her arm climbing out of her crib, and I realized that the distance from the top of a crib rail to the floor is a long way for a small person to fall.
Yep, your husband is right: Your son will indeed climb out of anything that's not a crib. You'll have to walk him back to his room a lot at first and maybe even put a gate on his room door. But the novelty of getting up is normal (though a pain for parents) and it's a phase that does end. It's going to happen whenever you make the change so why not deal with it now rather than later? Good luck and I hope you find him a good bed he can use for a while.