Guys,
If you buy Quake now on Steam, do you need the Steam client to launch it?
Or you get the whole package and can use it independently from the Steam client?

You need to buy pak1.pak, needn't you? The shareware version contains only pak0.pak, right? So if I buy it on Stream, will I get the pak1.pak file?

You get pak0.pak and pak1.pak, without further need of Steam.