A minimal Linux installation requires a machine for which a port exists, at least 2Mb of RAM, and a single floppy drive. But to do anything even remotely useful, more RAM and disk space are needed. Refer to: "Ports to Other Processors.", "Disk Space Requirements: Minimal, Server, and Workstation.", and "Minimum and Maximum Memory Requirements."
Intel CPU, PC-compatible machines require at least an 80386 processor to run the standard Linux kernel.
Linux, including the X Window System GUI, runs on most current laptops. Refer to the answer for: "How To Find Out If a Notebook Runs Linux." There are numerous sources of information about specific PC's, video cards, disk controllers, and other hardware. Refer to the INFO-SHEET, Laptop HOWTO, and the Hardware HOWTO. ("Where Is the Documentation?")