Kitchen cabinets - what thickness and type of backer board should be used?
You have to remove the plaster &amp; lathe to do "backer boards" as they go between the studs &amp; are typically 2x4's or 2x6's. If you're leaving the plaster &amp; lathe then you're talking more about a Ledger or Hanging Board that gets screwed to the studs &amp; just sits on the face of the lathed plaster.

These are typically just 1x6's or 3/4" plywood strips &amp; should be shimmed to straighten &amp; flatten the wall for the cabinets. You'll need to fill the end cabinets' gaps if using this method or skin the cabinet sides &amp; scribe those to the wall.

However, you really shouldn't need either &amp; you should be able to hit 2 studs for each larger cabinet's top &amp; bottom. Use Beefy Coarse Thread Deck or Wood Screws, not drywall screws. In the case of small 12" wide type cabinets, they will be screwed to the bigger cabinets &amp; supported solely by them.

Molly bolts, Mushroom-Heads or Spreading Anchors can be used just to suck them against the wall. Screw everything loosely to start with &amp; then shim the cabinets to perfection beside the screws before sinking them. Use an impact driver if possible, this will sink the screws better &amp; avoid chewing up screw heads.