Checking raw data is of course good airmanship, but it is not required by EU OPS, at least not in all cases. We do not have to check and monitor raw data on NDB and VOR approaches if we have 2 FMC and database selected approaches. It is however still recommended (and most just display the RMI-needles on the ND). It is required to check and monitor raw data on LOC approaches and non database selected ones.
Putting relevant points for the procedure and missed approach onto the ND is of course allways a good idea, easy to do with the fix pages on the 737 and if you do not have any procedure you can select a runway and a runway extension which helps. But dont go too much heads down in the last minute, if you have to switch in the last moment just switch off everything and fly it manually raw data, basic flying is sometimes still required and actually quite a lot of fun.