I guess you currently have either a corrugated plastic, or more likely, a polycarbonate roof covering.
The timber structure carrying this is very unlikely to be enough to carry any "conventional" roof. There will be "self-weight" loads from adding plasterboard and plaster for a start. Existing timbers could be strengthened, or removed to make way for more substantial joists.
EPDM is a very good, long lasting solution. Very much the way to go for a modern flat roof. It would have to be carried on a new plywood/chipboard deck which would also add load to the joists though.
Strip the whole lot off and start afresh, I would say. As to cost, flat roof would be quite a lot cheaper than constructing a traditional "cut roof" with slate/tile covering.
With a cut roof, you would have the additional cost of dealing with the side cheek gables. (triangular bits on each side of a raised, pitched roof.) Insulation is easily fitted within a slate roof in the usual way.
For a flat roof, go for a "warm roof". Celotex board insulation fitted on top of the new joists. Then the timber deck, and finally the EPDM.