I'm going to bake this cake: http://www.epicurious.com/recipes/food/views/French-Yogurt-Cake-395471 and was wondering what sort of vegetable oil (canola etc) I should use? Would the type of oil make any difference to the cake?
The kind of oil you use in baking is mostly a matter of personal preference. Any neutral oil (no strong flavor) will do.
I suggest you use an oil that you keep around for another purpose, which is not too expensive.
Some good candidates include:
Grapeseed oil is also excellent but tends to expensive.
Oils you would want to avoid due to the fact that they bring more flavor which may not be what you want in baked goods include:
I recommend canola oil when I'm required to use oil, but I recommend using butter instead it taste more homemade.