I have a VAT floor and want to tile over it. I've been told 5 different things to do ranging from remove the tiles yourself to tile over them. Since budget and family safety are most important I will tile over. It's a small area. About 4x8'. Questions.

Am I doing the right thing?

Do I put down backer board? (tile on concrete and in good shape.

Thoughts?

Thanks,
Kevin

Peoples fear of having asbestos removed professionally is unfounded because of cost. Removal of this small amount of asbestos tiles would not cost very much.
However removal of these tiles yourself is not a hard or unsafe project either. You simply need to wet the floor and keep it wet while removal of the tiles take place. The dust created is what the safety issue is with this type of tile. Keeping the floor wet will prevent any dust from getting into the air. Disposal of them is simply plastic bags and contact your local township dump. They will tell you how to dispose of this garbage.

AS far as covering them you can do this also. To install backer board or cement board over a tiled on cement slab floor you must drill the floor to screw the board down. That causes dust as you drill. This is what you want to avoid with the asbestos in the first place. So this method of covering them will not work.
If the tiles are strongly attached and in good shape and you do not want to mess with them do this,
Purchase Schluter Ditra Mat, It is sold at most Home Depot stores. Its orange and looks like an egg crate on one side and a felt cloth on the other. It comes in rolls. One roll will be enough for this size project.
You use Un-modified thinset mortar to fasten it down with a knotch trowl. Do not use modified which is typically pre-mixed tile cement. It will never dry.
Once this is down put what ever tile you like on the floor. But again use UN-modified mortar to set tile. You can get this cement in white or gray. A marble saddle at the doorway will be high enough to finish off the edge of the tile.

Thanks for the advice. As much as I would love to remove the old tiles it just isn't possible with the new carpet and heating/boiler already in place. I will try this system. Do I leave a gap at the edges or tile to the wall?