MainStage would work great for this, and its really affordable at $30! You could create a patch for each song, with each patch acting as a container for a plug-in called PlayBack, which would in turn contain a song's soundfile. When you select the patch it would play instantly. You could apply any eq, compression to the output if needed. You would also have a volume control (or controls for eq, compression, etc if needed).
You would have to spend some time reading the manual, and set up a custom layout for what you want, but it wouldn't take long.
Logic Pro 9.1.6 with Lion OSX. Mac Mini Server 2.0G quad i7, 8G RAM. MOTU Ultralite mk3 firewire I/O (live), Apogee Duet 2 (studio). Controllers: SoftStep pedal, Alesis Trigger I/O, Korg Nanokontrol, WX5 wind. A bunch of plug-ins. Some duct tape.