[GIS] Distinct color fill for each feature

Question

I'm building my first map, so please forgive me beginners mistakes.
I've downloaded QGIS 2.0.1 and following tutorial I was able to download data from http://sdi.geoportal.gov.pl/wfs_prg/wfservice.aspx?request=getfeature&version=1.1.0&service=wfs&typename=WOJEWODZTWA and present is as one layer in application.
My SHP file has 16 objects (Polish provinces).

My problem is that right now I have one layer (with one layer style) and I can show/hide all provinces at once, what I want to do is to have all provinces as layers (or groups) so I could show only some provinces and change their color.

I know that I can select shape using select tool, then export selection into SHP file and import 16 layers into project.
This is fine when layer has 16 objects, but my second map has over 3000 districts and I must be able to hide/show/change color of them individually.
Can this be done better/faster?

EDIT
I managed to split my SHP into layers, this way I have 16 layers and I can add style to every layer individually. I can also hide layers using layers panel.

Can I add similar select to layer? So I can choose which object to show/hide?

Answer 1

For distinct coloring, Rightclick on the layer -> Properties, Style tab

Change single symbol to categorized, select the name field (or ID if you want), then click on Classify and OK.