You will have a much harder time with Quake if you chose to use another engine. The Quake Configuration guide expects you to use one of these two engines. They are both actively developed and fantastic choices to play Quake with. DirectQ puts a lot of focus on ease of use and user-friendliness.
Quakespasm has more features and a well-tested code base. Both support using files for the soundtrack (as opposed to having your CD in the disc drive all the time). DirectQ runs very well on modern integrated graphics adapters like for example the Intel xxxx, it uses DirectX (instead of OpenGL) so it is a good choice for AMD/Ati users as well. ChunkyPPC, P96-PiP, CD-Audio, Joypad, Joystick, etc.) and for. Steffen Häuser, for his help to port Quake and QW (for example. THANKS - id-Software, for releasing the Quake and QW source under GPL. Quakespasm runs on Windows, Linux and Mac, DirectQ is Windows only. all mails concerning standard Quake/QW to Steffen Häuser. Try both to see which one is the best Quake engine for you. They both strive for faithful looks, useful features and support for modern maps and mods.
Quakespasm and DirectQ(inactive link: see below) are recommended engines. vkQuake seems popular (it's a Quakespasm fork). Quakespasm is still a good choice, Quakespasm-Spiked probably an even better one.