Get at least 500 MB, preferably 1GB or more, and you will not regret it. Add more memory, more hard disk, a faster processor and other stuff depending on your needs, wishes and budget to go beyond the merely usable. In general, one big difference from DOS is that with Linux, adding memory makes a large difference, whereas with DOS, extra memory doesn't make that much difference. This of course has something to do with DOS's 640KB limit, which is completely nonexistent under Linux. Ports are also being done to the ARM, StrongARM, and MIPS architectures.
More details are available elsewhere.
Linux puts higher demands on hardware than DOS, Windows, and in fact most operating systems. This means that some marginal hardware that doesn't fail when running less demanding operating system may fail when running Linux. Limited Token Ring support is available. Most 16450 and 16550 UART-based boards, including AST Fourport, the Usenet Serial Card II, and others. Some ISDN, frame relay, and leased line hardware is supported.