Once you get your ignition worked out, good fuel helps a lot!
My mule was always a cranky starter, I was using regular unleaded with additives and stabilizer.
I ran it sometimes on ethanol free aviation fuel, on which it started better, but ran rather hot.
Recently, I'm able to get ethanol-free fuel at several filling stations locally, so now use that exclusively in the Mule. It made a huge difference in ease of starting and how it runs. The Mule seems very happy with the change.
Back when I drove Mules in the Marines, our start procedure was -
Full choke
Ignition switch off
Four pulls on the starter rope
Ignition switch on
1/4" to 1/2" of choke (depending on the likes of the particular Mule)
Pull the starter rope and it fires right up
My personal Mule has electric start. Following the same procedure, but substituting a quick 1-2-3-4 count while pushing the starter button instead of the rope pulls with the ignition switch off, achieves the same results.
Mine likes 1/4" of choke.
Cheers