Difficult to suggest a suitable FPGA without knowing more about your project. Some microprocessor cores (such as PicoBlaze) fit into a tiny FPGA. Even the 32-bit MicroBlaze with hardware floating-point fits into the small XC3S200 on the Xilinx/Digilent Spartan-3 Starter Kit.
The Virtex devices are all BGA, and require somewhat critical PCB construction. A Spartan-3E (or some other Spartan-3) is more forgiving, and some packages can be hand soldered. They aren't as powerful as Virtex, but are much cheaper and perhaps a better choice for a first project.
Xilinx's two major distributors are Avnet and Nu Horizons. Ordering from them is almost as easy as DigiKey, if you know the part number.
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Xilinx's iMPACT software talks to several Xilinx cables: the old Parallel Cable III, Parallel Cable IV ($125 US), Platform Cable USB ($199 US), and the old MultiPRO. The Parallel Cable IV and Platform Cable USB are fast, expensive, and proprietary (no cheap clones). The Parallel Cable III is easy to find cheap clones, or build yourself. I don't know about the MultiPRO.
Other USB-JTAG products exist (such as from Digilent), but they require their own download software, and generally won't work with Xilinx software such as iMPACT and ChipScope.
Xilinx's iMPACT can be configured for a custom JTAG chain. I would expect Digilent's USB-JTAG products (and other company products) to be configurable too, but I've never tried them.