Most of the sites I've been to list the bit depth and sample rate. What sites are you not finding this information on?
If you're downloading WAV, AIFF, FLAC or ALAC they are all lossless formats and are generally 16/44.1 or higher. If they are higher resolution than 16/44.1, they are normally priced higher and because of this most always indicate whether 24/44.1, 24/48, 24/96, 24/176.4 or 24/192.
Knowing the bit depth and sample rate for lossy MP3 doesn't tell you the level of compression, so the bitrate is the indicator of relative quality for these files. You can have MP3s that all show 16 bits and 44.1KHz in a player, but the bitrate column showing 128kbps, 256kbps or 320kbps would indicate the compression level and relative quality. If the MP3 is encoded as VBR Variable Bit Rate, the number would be a bit less than those exact numbers.
Steve