Typically, iPhoto stores photos in the home folder->Pictures->iPhoto Library if you have iPhoto '08 or later. In order to see the picture files, you will need to right click on this file and select "show package contents". With earlier versions of iPhoto, you can see all the "child" folders inside a folder called just iPhoto. BTW, for some reason or other, I also have an iPhoto folder in my Documents folder - an earlier version of iPhoto put it there as far as I know. I need to move the pics from that into the later version...or I could just move 'em all to Lightroom, since that's what I'm using these days. Anyway, if your Macs are networked, you can import the older file by simply pointing iPhoto to it.
Bookmarks for Safari are in your home folder->Library->Safari->Bookmarks.plist
Bookmarks for Firefox are in home folder->Library->Application Support->Firefox->Profiles->(some random letters)default->bookmarks.html
You should be able to import both by either pointing the Mac mini to the files (assuming the old and new Mac are networked and file sharing is on) or by copying both of those files to the mini and then importing them from the "import bookmarks" menu item.
The Address book data is also in the home folder->Library->Application Support->Address Book. You can export an Address book archive and then import that into the new version if you wish. Don't know if that's the easiest method or whether simply moving all the files is easier.
Did you not use Migration Assistant? When I got my new Mac in November, that's what I did and all of these things imported without a hitch.
