Well I am going to depart from the norm a bit and ask why a semi-auto? A .22 makes good sense as a starter handgun, but why not a revolver? Want to start with a center fire handgun? Then why not a good medium framed revolver in .38 Spl. or .357 "Oh how Fuddish" some may reply, but here are the advantages as I see it:
1. simplicity: the manual of arms for a revolver is very simple. open cylinder, insert cartridges into chambers in cylinder, close cylinder. handgun is ready to fire
2. Trigger options: a double action revolver allows for two fire modes: single action (where you thumb cock the hammer, then pull the trigger) or double action (pull the trigger) using the single action mode will teach you how fire precisely and you can work on the fundamentals of marksmanship.
3. Reliability, when a revolver malfunctions, it is usually a pretty serious event, the upside of this is that revolvers rarely malfunction.
4. Variety of ammunition: revolvers will feed a variety of bullet weights and shapes, no worries about having pet loads...also cartridges can be loaded from "mild to wild."
5. Versatility, a .357 magnum revolver can shoot both .357 magnum and .38 spl calibers giving you a variety of options
6. Availability: plenty of used revolvers in .38 and .357 available at fairly attractive prices
7. Maintenance: no elaborate field stripping with springs flying everywhere: simply clean the barrel and chambers, lubricate at a few key places and wipe down the gun and you're done
8. Safety: to see if the revolver is loaded, simply open the cylinder latch (you can also look at the chambers to see if the gun is loaded, but I don't like to point a gun at myself in such a way as to do that, that's up to you.)
9. Mature technology: modern double action revolvers have been around since the 1890's and all the reputable manufacturers have pretty much ironed out any bugs in the operating system
Food for thought, anyway.