... We would also like the capability of transferring points to a topographical map of the cemetery.
Computer connectivity is mostly a standard feature these days. Mapping units often come packaged with topo maps or free maps are available for some brands.
We would like to keep costs as reasonable as possible but would be willing to invest in equipment that would be appropriate.
Given the accuracy you can expect from recreational grade units I don't know that they could replace your metal detector for finding the corner markers. Unfortunately GIS grade (sub metre accuracy) or survey grade (sub centimetre accuracy) are much more expensive.