In ArcGIS 10, if you go into, for example the Data Frame Properties, and go to the "Predefined" co-ordinate systems, you can click on two co-ordinate systems you mentioned in the question - OSGB 1936, and British National Grid, if you click "Modify" on both you will see that they actually both use the OSGB 1936 Datum (click on "Modify" again on BNG to see the Datum).
You probably want to use the British National Grid Co-ordinate system, because it is the basis of all OrdnaceOrdnance Survey Grid references- basically the projection is a set of mathmatical formulae that maps real world positions onto the co-ordinate system that is used in the UK. Not entirely sure what the OSGB_1936 co-ordinate system would be, but the major difference between a geographic and projected co-ordinate system is that:
"Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions" (ArcGIS 10 Help File).
This obviously makes it much more useful for precision applications such as plans, although this accuracy will generally only be high over a relatively small area compared to a geographic co-ordinate system, which is suitable for describing a point with (relative) accuracy over the whole earth's surface.