you can have it in 2 ways.
the easy one is to extent your web application and basically all problems solved, since you have all ur data with an anon face.
but if you want to have 2 different site collections, 1 anonymous for the public facing and another dedicated for the catalog(s) then there is a catch - for the items themselves of the cataloged list you can leave the anonymous access and everything will be alright, but if you use the dedicated site's resources than ur in for a login promt. and giving the anon users lists and libraries only doesnt fix that, so ur in for 2 anon sites.
for example i have 2 catalogs lists, one have its images as links and secondary as images from an image library. the 1st list items are shown in the public site, but the 2snd list items are not unless i give it full anon access.
and dont forget - you must also cancel the break inheritance in the master pages gallery, and either publish all the new stuff or cancel versioning (the publish/version is everywhere actually)