If you can afford the 1GB, then by all means get it. If you just want the bare minimum, don't go any less than 512MB. I recommend keeping the 1GB. It comes in handy when you doing a lot on your computer.
As far as the modem goes, get something cheap like this:
U.S. Robotics USR263090 56Kbps PCI Bus (Plug and Play) Internal Modem
They're pretty good. It's dial up technology so there's really nothing you can do to improve connectivity.