If you want Network Neighborhood in Linux you could install Samba but i sugest don't do that (hard to browse)... There is also NFS, but don't do that either. (NFS=Nightmare FileSystem
). I stick for now to the ideea of installing a FTP server. Then edit /etc/vsftpd.conf (for vfFTPd daemon) and create a anonymous access directory and... you'll see there what you can do. If you don't want anonymous access you can create users on both computers and let them login to their home directories (and more if you wish).
I'll others with more experience to give more advices. (and probably better)
Hoped I helped.