Some Silverstone Lascala HTPC cases have optional rack ears. But if you want a purpose-built rackmount case, the Antec Take4 (designed, in fact, for audio production racks) was well reviewed a few years back but isn't widely available anymore. It'd be easy enough to quiet down any El Cheapo 4U case though, they are already sturdy thick steel to avoid vibrations and they usually have good ventilation. Looking at a cheap 4U on Newegg, the Ark 4U-500-CA
, it already bodes well for quiet computing with the filtered door over open 120mm intake and dual 80mm exhausts. The hard-mounted HDDs aren't ideal but you could easily put several laptop drives on adapter rails. (or suspend them but that isn't ideal for oftenly transported cases)
Just be smart about the components you put in, and DEFINITELY swap out the stock fans for better stuff.
ETA: If you are looking for a 3/2/1U case it shall be a far greater challenge. They use smaller nonstandard power supplies which are bound to be loud and difficult to find replacements for. Also they tend to use smaller screamier fans.