Nothing plays APE. FLAC or ALAC (or WAV or AIFF uncompressed) are your only (realistic) options if you want to play the files without first converting.

You should probably evaluate what your management/handling/playback ecosystem looks like before deciding. Though it should be straight forward to batch-convert between formats at a later time if you need to.

One more thing... The table/wiki linked above contains a number of inconsistencies and out-of-date information. ALAC and FLAC have decent hardware support. At least any hardware product that matters supports one or the other or both.