From a guy who has run 1" axles....
Go with the 1-1/4" , 1/4" wall chromoly.
The 1" solid is actually stronger, anyone who tells you otherwise is wrong
However, the 1-1/4" bearings are smoother & when your at the track and you tear something up your going to have trouble finding parts for a 1" axle! I had problems at a race with 1oo+ mowers, about 3 of us had 1" axles!
On shaft locks. get the 2 piece split locks, not the solid set-screw type. You can also buy them without a key-way in them. http://www.mcmaster.com/#6436k74/=s6bi9i