Linux/Alpha is known to run on machines with as little as 8MB of RAM and a 170MB harddisk. In those 8MB of RAM, you can run Emacs-19.28 without swapping, but that's about it. A system with 16MB RAM and 500MB is perfectly reasonable to work with, even when using X11. 32MB RAM and on the order of 1GB of disk should satisfy even power-hungry users, though, as usually is the case: the more the better.
(Well, I guess one's perception of what is reasonable can change with
time, and with DRAM prices. I know that by now many people would consider
32MB the bare minimum, 64MB usable. Recent releases of RedHat seem to need
at least 24MB just to install...
And you'll have a hard time looking for a hard disk smaller than 2GB.)
Note that, though many Alpha mainboards support EIDE, performance is reported to be unsatisfactory. SCSI is recommended.