As I read thru all the suggestions, I see a major problem.
First gun and new to shooting.
With that being stated.
First gun in a handgun should be a wheelgun in .22 long rifle; and about a couple cases of .22 ammo. After he/she feels that they are proficient with .22 caliber handguns then they move up to larger calibers.
New shooters should also consider getting into reloading. I have shot for over 40 years now and have been reloading that long also. Having loaded everything from .380 acp to .50 BMG with tens of thousands of rounds of .40 S&W and 10mm on progressive presses. By reloading your shot groups will get smaller, and cost to make your own rounds are normally a quarter of that of factory ammo.
Best defense caliber - 9mm, 357 mag, 40 S&W, 10mm, 45 acp ?
They all work great, depending on shot placement by the shooter.
A consistence shooter with ANY caliber is more lethal then which caliber or what weight bullet they are shooting. I shoot mainly .357 mag, 40 S&W, 10mm, and 45 Colt in both semi-auto and revolvers. I also would also feel comfortable if I only had one of my .22 LR pistols if that was what was at hand. Repeat shot placement, recoil recovery, and feeling comfortable with what your are carrying are a lot more important than big, or small calibers. I personnally like the 10mm and either carry a semi-auto or a revolver in that caliber.
Practice, and practice offen. I normally run miniumal of 200 rounds a week at the range, for any day that I shoot. Cost does factor into the totals of what you can do. In the efford, you would be wise to look into reloading what you are shooting. Pickup your brass at the range; in fact pickup all brass at the ranges, it is good trading material if you are not shooting that caliber, others do. Costs to reload is 1/4 or less of buying factory rounds. Calibers do not matter, as components costs are about the same for all. It might cost a little to setup at first, but the pay off is great. The more you can afford to shoot, the more you can shoot. Try to find a friend whom is into reloading to help you get started.
Safe shooting.