I would get an opinion at the tile store, but I can't see what the problem would be. 3/4" subfloor should be a pretty good base.

You need to start with the joists - size, spacing, and span (and that they are in good condition). This site http://www.johnbridge.com/vbulletin/deflecto.pl will give you a rough idea if your joists are stiff enough for tile (I couldn't get it to accept the URL for this as a link).

If not, then you need to reduce the deflection - either sister the joists or add a support beam.

3/4' plywood is probably OK, but the recommended thickness is 1-1/4', so an extra 1/2' of plywood on top of the existing subfloor would be a good idea (glue and nail the top layer to the 3/4' plywood - not the joists). If the height buildup gives you problems, you can glue/screw strips of plywood to the bottom, and nail cleats into each joist (not easy - been there, done that).

I'd use 1/4' cement board on the floor (over a bed of modified thinset). Its purpose is to give a good bonding surface for the tile - it doesn't add any stiffness or flexural strength to the floor.