A mix of brick an stone looks good, purely a personal choice, most brick manufacturers make thin brick either cut down full size or cast in thinner profile. There are a number of "fake stone" manufacturers out there, i would not got with any vinyl stone prefer cement type cast stone more durable; look at Culture Stone, El Dorado to name a few they have a wide selection of stone types.
You can do a mix of these both are applied over lath with a scratch coat, thin brick typically needs a brown coat to create a more level base.
I'd recommend you explore using an AWRB ( air water resistive barrier)on you sheathing to prevent potential damage from incidental water intrusion. You'll want one that is self sealing the holes from fasteners for trim and lath, NOT TYVEK or ZIPWALL!!!. Take a look at mag oxide (Multi Panel) sheathing a bit more expensive but non combustible and vermin proof. Dupont makes a product called ArmorWall very nice option giving you CI ( continuous insulation) again a bit more money, CI is most efficient way to insulate your home.
Whatever you choose be sure you contractor is reputable use high quality awrb and installs flashings to manufacturers recommations.
Like everything else buy once cry once.
Be glad to answer to any questions you might have, I work more on commercial side but residential is pretty much the same in principal.
