Who's on First?

There are several calculating machines that are claimed to be the "first computer".  These claims depend on what is meant by "computer" and, to some extent, on what is meant by "first".

Among the contenders for "first computer" are Charles Babbage's Analytical Engine, Konrad Zuse's Z3, Tommy Flowers' Colossus codebreaking machine, The Atanasoff-Berry Computer, Howard Aiken's Harvard Mark I, Eckert and Mauchly's Eniac, The Manchester Baby, The Manchester Mark 1, Maurice Wilkes' Edsac, and The Pilot ACE.

• Charles Babbage's Analytical Engine
• The first programmable computing device
• Mechanical (gears and numbered wheels)
• The first computing device to have a program written for it
• The first computing device to use punched cards
• Turing complete (can perform loops and conditional execution)
• Only a partial version was built (the Difference Engine)
• There is a proposal to build a complete version
• 1837
• Konrad Zuse's Z3
• The first Turing complete electro-mechanical programmable fully automatic digital computer
• Electro-mechanical
• Programmable
• Turing complete
• May 1941
• The first English translations of Zuse's work were done in 1965 
• Tommy Flowers' Colossus codebreaking machine
• The first electronic digital programmable computer
• The first use of parallel computing
• Electronic (relays and vacuum tubes)
• Programmable
• Not Turing complete
• December 1943
• The Atanasoff-Berry Computer
• The first electronic digital calculating device
• Electronic
• Single purpose, not programmable
• Not Turing complete
• Never built
• 1942
• Howard Aiken's Harvard Mark I
• The first automatic digital calculator in the United States
• The first digital computer to gain popular attention
• The largest electro-mechanical calculator ever built
• Electro-mechanical
• Programmable
• Not Turing complete
• An insect trapped inside the Mark I was referred to as the "first actual case of a bug being found" by Grace Murray Hopper who was fixing the computer  
• May 1944
• Eckert and Mauchly's Eniac
• The first Turing complete electronic digital computer
• Electronic
• Programmable
• Turing complete
• July 1946
• The Manchester Baby
• The first stored-program computer
• Stored-program
• Electronic
• Turing complete
• 1948
• The Manchester Mark 1
• The first use of index registers
• Stored-program
• Electronic
• Turing complete
• April 1949
• The first commercially available digital computer, the Ferranti Mark I, was an improved version 
• Maurice Wilkes' Edsac
• The first implementation of subroutines
• Programs could be coded in the first assembler
• Stored-Program
• Electronic
• Turing complete
• May 1949
• The Pilot ACE
• The first use of floating-point arithmetic (implemented in software)
• Initial design by Alan Turing
• Stored-program
• Electronic
• Turing complete
• 1950

The are simulators for the Analytical Engine, the Zuse Z3, the Colossus codebreaking machine, the Atanasoff-Berry Computer, the Manchester Baby, the Manchester Mark 1, the Edsac, and the Pilot ACE.

There are also mechanical models with instructions for Difference Engines using Lego and Meccano (including images of a Difference Engine #2, but no instructions).