The "Quick Logon" setting only affects when the client authenticates persistent connections: at bootup when there's a ton of stuff going on vs. first access of the drive, when your machine's probably not quite so busy. This *shouldn't* affect browsing, but like you said, this is Windows we're talking about... ;p
If you do *not* have a WINS server on your network for name resolution, the other methods are: lmhosts lookup or broadcast. lmhosts lookups can be used, but the lmhosts file must be maintained manually on each machine. This may be doable for a small network, but as your network grows, it very quickly becomes unmanagable. Your machines can also perform name resolution via broadcast, but it cannot resolve across networks and is very inefficient (when booting a machine, it can take 5-10 minutes or more before you are able to properly browse your network - sound familiar? If you want to understand what's going on behind the scenes WRT what you're trying to do, take a look at the Browsing and Browsing-Config files in the docs area of any of the Samba mirrors... some of it's kinda dry, but it'll give you an idea of the process involved).
The easiest way to take care of all this is to have a server in place to take care of DHCP/WINS in addition to file sharing. One other thing you might want to consider is how to devise a backup and recovery plan for a peer network with critical data files over multiple machines and directories (not trying to poke fun of you, I've been there
If you go on the assumption that this server will be up 24/7, you can provide connectivity and browsing regardless of which clients are up or down and with just one point of failure (as opposed to many, many peer machines), you can put UPS/tape backup/recovery procedures in place for a couple hundred $$ (or less, if you are good at scavanging).
Good Luck!
Bob