Most transparent, trouble-free linux and Windows filesharing

Samba is probably the best way. There's a learning curve, to be sure, but in the long run it is probably the easiest and most standard way for a bunch of windows computers to get at files off of a Linux server. Most Linux distributions should have a "default" configuration which you can use to get 90% of the way to where you want to be.

Otherwise you could use WinSCP in Explorer mode and people can get/put files that way.

There is also a Filesystem-Over-SSH tool for windows, but I've never used it.

NFS on Windows is probably a bad idea -- it has been in the past. Every time I've tried it I've had performance and access problems galore.

Maybe iFolder comes pretty close to what you are looking for.

Unfortunately, there aren't official packages for Ubuntu AFAIK. Anyway, here's a step by step guide to set it up on Ubuntu 9.04.

Look into a NAS dirtrobution such has FreeNAS (Based on FreeBSD) or OpenFilter (Based on Linux). They really do make sharing files simple and even help with back up.

I personally have been using FreeNAS at home serving NFS, Samba, iSCSI (for VMWare) for a while now.