Id avoid using winquake or dosbox these days, they both have limited resolution and framerates, and wont play the game's music (unless you have an original CD lying around).
The Quake Starter Package is probably the easiest way to get the game setup these days, it comes with Quakespasm-spiked as a source port.
And based on those pc specs you should have no issue running the game, even some graphics mods should probably work fine.