I cannot “prescribe” what is the better choice for you, but will give my thoughts on this:
Ammo: Right now, factory 9mm ball can be had at significantly less cost per box/case than can .45 ACP in the same configuration. If you buy your range ammo, this is a big plus for 9mm as you can afford to do more shooting and with proper practice you should become a more proficient user of the pistol than if you shoot less often due to ammunition costs.
If you intend to reload for your centerfire, I’d go with the .45 ACP. Accurate loads abound and can be found using cast, plated, swaged, and jacketed bullets in low, medium, and higher velocity loads. I’ve had an easier time finding truly accurate .45 ACP loads with cast bullets than with 9mm. If you do intend to reload and use primarily jacketed, go with the one you like best. The 9mm can be capable of surprisingly tight groups with loads the particular gun “likes.” It will cost more to reload for the forty-five than the 9mm, but it’s considerably less costly than using factory ammo once you’ve amassed empty cases, equipment, etc.
Pistol Selection: There are quite a few choices in either caliber, but I believe you will find more in 9mm than in the larger caliber. Both calibers can be had in handguns ranging from “compact” to those of service configuration.
Self-defense Considerations: There are a number of very, very good defensive loads available in either caliber. Both offer expanding bullet loads in both standard pressure and +P, with some +P+ 9mm loads being available. While I do believe that with the better loads, .45 ACP is probably the more potent of the two, I do not believe that its “superiority” over the 9mm with better loads is a great as some might have us believe. Placement remains the primary determinant in “stopping power” in my opinion.
This 230-gr. 45-caliber Golden Saber expanded nicely when fired from a 5″ Kimber 1911 pistol. I think it would make a very good defensive round. It also feeds reliably in most pistols. It is a standard pressure load. Average velocity for this lot of ammo was 870 ft/sec.
These 9mm Winchester 127-gr. +P+ Ranger SXT bullets were fired from a Browning Hi Power. The one at the top was recovered from a deer. The one at the lower left was fired into wet pack and the lower right, into water. From the Browning, these average 1269 ft/sec.
IF self-defense is your primary focus, go with the pistol that is reliable and that you can hit best with. If there’s no difference, I’d go with the forty-five. If you prefer the extra shots sometimes available in some of the 9mm’s, go with that. Either has what it takes to do the job IF you can get the hits. All commonly-used defensive handgun calibers are weak compared to even the lowliest centerfire rifle round, but most possess “enough” to do the trick for physical rather than psychological reasons if properly placed.
“Either-Or” Considerations: For varying reasons, I find that some shooters want either a 9mm or a .45 ACP. If price is the determinant, I’d go with the 9mm. Buy the best gun you can afford in it; the savings will be realized in the ammunition savings IF you intend to shoot it more than just for familiarization. If you want the low-cost shooting, but do not trust the 9mm to be effective, go with the larger caliber. The reason I cannot understand is that some 9mm shooters refuse to own a forty-five and visa-versa. I see no reason not to unless cost is a major consideration. I like both and see both advantages and disadvantages to both. Neither is perfect, but neither does the use of one require abstinence from the other.
Best.