I have a small underpowered desktop running in my house that only has onboard graphics and it runs Ubuntu 16.04 just fine, but its only connected to 1 monitor, not 3.
The Intel integrated graphic card of my laptop does handle 3 screens fine and I dont need to mess with drivers, everything works well out of the box. I would actually advise against NVIDIA cards unless you need powerful graphic processing or to do GPU computation.
Cool. Didn't know laptops existed with 3 monitor ports. Which model laptop are you using, and would you recommend it for programming? :)
Ahhh, doing some Googling shows it's from add-on peripherals and/or docking stations. eg: