If you want to do miniatures, you need a resin-based printer, which can print with higher quality than filament-based models. Expect to pay $1,500 for one, although there are a couple of tiny resin printers still in Kickstarter / early production phase that are around $700-1000.
Filament printers are cheaper, but the quality is poor - here's a good example of Da Vinci 1.0 ($500) print quality:
https://gigaom.com/wp-content/uploads/sites/1/2014/12/img_6036.jpg - on the positive note, while quality is poor, you can print objects up to 20
cm / 8" in size, though the max. size print takes something like 8-12 hours, depending how complicated the design is.
Of course you can always have a low-quality one at home, and order high-quality prints from Shapeways etc., but those are not cheap either.