FreeSpace 2 is widely regarded as one of the best games in the genre. You will likely want to install
fs2_open with it, which will improve the visuals significantly.
Diaspora is a BSG-themed mod for FS2. Ships have Newtonian flight physics, which can take some getting used to. It is short, but is easily my favourite game in the genre. Don't fly into flak.
If you're not put off by aging visuals, then Tie Fighter and XWing are two good (but quite old) DOS games in the genre. GoG doesn't sell them, so you will likely have to grab them off TPB, and set up DOSBox yourself.
I haven't played it, but the
Wing Commander series is well regarded. Unfortunately the sprite system used for drawing ships hasn't aged nearly as well as the 'shaded polygon' method used by XWing and Tie Fighter.