Welcome ian,
I am interested in creating a tile-based game, is the WME engine the right choice for this?
it is required for a home design application that has been created in C#
Well, WME is actually designed for creating 2D adventure games, anyway it is actually possible to create tile based games with it, but you won't find too many exisiting examples here and it could cost you some effort.
For example another non-adventure game "Wilma Tetris" (
http://dead-code.org/misc/wtetris.zip) was done with WME, and there are some games in development which use keyboard control of the actor, too. I'd say it depend on your ideas in detail. So... I guess it IS possible in general and if you decide for it, your questions are always welcome - but it's not originally designed for it.
I can't recommend any other game engines for it since I simply don't know them. I heard BlitzBasic might be a good choice for it, but I simply can't judge it due to missing knowledge of mine about it.
Good luck, what ever your choice will be.