A few ideas on going driveless, I dont think you would really need a gig of RAM. One thing you could do is just use a livecd version of linux. For some of my computers I use morphix(
http://morphix.sourceforge.net/modules/news/ ). They have a few different versions. The light version takes up the least space and still works pretty well. Once you burn on a cd you can then install it to a USB thumbdrive. I havent done it my self but I hear it will boot in like 5-10 seconds.
Or another option if you already have linux server going, you could set up a thinclient or I guess in your case a diskless client. The client would boot off the server and run through the server. I have a few of these at my house(whoever thought an old 486 compaq would ever be useful again???). To make these thinclients you would need to download LTSP from
http://ltsp.org . Then, to boot from the network you would either need a bootable NIC or you can use a floppy and floppy drive. To make the bootable ROMS you can go to
http://rom-o-matic.net/.
The second option is quite a bit more complicated but you can setup up multiple diskless clients. I have a small howto setup LTSP on REDHAT 9, but its still a work in progress.
http://linux.xyrka.com/howto/howto-setupltsp.shtml There are also many useful docs on the ltsp site. If you have any question feel free to pm me or just reply in the post.