What should I get, and from where, to be able to play first and second Quake, on Linux, in single-player mode?
DOSBox emulation usually works really well, particularly for the more popular titles, which get a lot of testing. And any even remotely modern PC should have the performance to emulate it easily. You'll probably even be able to do multiplayer (DOSBox has IPX/SPX emulation).
Quakespasm is a great fork of Fitzquake, the best (faithful) Singleplayer engine there is: http://quakespasm.sourceforge.net/download.htm
If you cannot use a OpenGL engine, maybe give Tyrquake a try.
You will need three components to make this work: A launcher, an engine, and a set of original data files. The latter may be the most annoying to obtain; however, a quick search suggests you can still buy an original game disc on Amazon.
Once you have that, install this package:
This launcher package will also pull in an engine and a tool to extract the data files off the game disc. Once done, you should be happily fragging away with minimal fuss.
The DarkPlaces engine is a very easy way to play Quake 1 on Linux. Simply type in
sudo apt-get install darkplaces into the console, and it will install. To play Quake, you will need to direct it to the base files. In a console, type
darkplaces -basedir /foo/bar/baz/,
/foo/bar/baz/ being the directory to the game files. Mind that this is not the
id1 folder, but the actual directory where the executible would be. If you just have the source file, put it inside another folder, like
quake1 or something that that. For RPM Linux distributions, I don't know how to use RPM, so I'm assuming that you can translate what I gave you to that.
EDIT: For what I know,
darkplaces only is obtainable by
apt with the Ubuntu repository.
You can play Quake through your web browser here: Quake Flash.
The Quake Epsilon build runs on windows, mac and linux (using the darkplaces engine) and has HD textures. You just need the .pak files from the full version of quake, which can be purchased off steam or gog.
Then you copy the pak0.pak and pak1.pak files from the id1 folder of the steam/gog version to the id1 folder of epsilon, and you're done.
In terms of Quake2, would not have a clue though.