Add a list-before field to $:/yourname/TiddlerTypeTemplates/Contact and set its value to $:/core/ui/ViewTemplate/body, then similarly for /Meeting. Take another look at Ordering Tiddlers if you don't remember how this works.

Setting list-after to $:/core/ui/ViewTemplate/classic would have the same effect, but I bet you're going to have no idea why you set the field to that specific value when you look at it 6 months from now. Saying it comes before body is much more intuitive. It also protects you better against future changes – if you used list-after and classic were to move to some other location on the tiddler display, your template might move around with it to a confusing spot. However, it's unlikely you will ever not want this template to appear right before the text of the tiddler, no matter where the text might move to.