I have not come across an optimal printer for the Surface 3. I had an older HP from 2010 that supported wi-fi and AirPrint, back when the latter was new. It served me well for the last 5 years but my fiance constantly had issues whether she used her MacBook Air, iPad mini, or Surface 3. We have since purchased a new Canon MX470 from Sam's Club. It was only $50 and came with a total of three black (one standard, two XL) and three color (one standard, two XL) cartridges. The price of the printer was essentially the same as a black and color cartridge for the HP printer so I didn't argue.
Again, I don't have any issues scanning or printing with it and my Surface 3 is my only PC. Like before, she has some issues but, as of late, I have been attributing them to user error. I don't really think it matters so long as you purchase a wireless printer. Windows 8.1 on the Surface 3 has automatically found every wireless printer on every wi-fi network I have connected to, downlaoded the appropriate software, and installed everything within a 15 second time period.