Software rendering will be SLOW.
The choice between DirectX and OpenGL depends on the card, and on your system.
A game I have, suggests that DirectX is the best choice for most cards, while OpenGL is better for Nvidia-based cards.
However, though I have an Nvidia based card, I find the OpenGl setting to be troublesome (leaves many blank buttons in the taskbar on exit, and crashes rather too often), so I use DirectX instead.
Some other cards were notorious for having poor OpenGL drivers.
One additional interface you may see mentioned, is GLIDE - the application interface of the old 3dFX Voodoo cards - and if that's the ONLY graphics acceleration a game (old, because it's obsolete) supports, then you need to find a "Glide wrapper" or Glide emulator - normally called a "wrapper" though.