You don't chip out all the old plaster!! They apply it over the old plaster. They do a bondcoat and prep it. Removing any spots in it that could cause for pop ups.
Our basic tile is the K-Series solid tile. At $30 a foot, that must be a really high end tile. When you quote these things you can't say one price fits all.
The plaster quote seems good for my area.... but check references and if they are current with good results...go with them.