Congratulations on the new Ithaca! They are getting to be very collectable and valuable. Yours looks like a very nice one.
Recoil-operated semiautomatics need ammunition loaded to a certain pressure level to function reliably. The .45 ACP's standard loading since 1905 has been a 230 grain round nose jacketed bullet loaded to about 850-860 feet per second. It is the bullet weight, shape, pressure and velocity that your Ithaca was designed to shoot and for which the sights were dimensioned to hit with. That has been the standard U.S. military loading since they adopted the 1911 and I would guess that, 105 years later, it is the loading produced, bought and shot in probably 75-85% of commercial .45 ACP ammo as well. Pretty well any ammunition company that loads .45 ACP loads that flavor of it.
I shoot primarily Federal's American Eagle red box and Winchester-Western brands when I buy it. It is very good stuff and I like their brass for reloading.
I carried Colt 1911's in .45 ACP at work for the last 22 of my 32 years on the job there. The department contracted with Federal for both training and duty ammo. I probably shot 40-50,000 rounds of the department's Federal AE45A during that time. I never had a single bad round.
Also, Remington loads it, Speer loads it, CCI loads it, foreign ammo makers load it.
My advice is to stick to factory loaded ammo from company names you recognize, and to stick with brass cartridge cases. There are brands that use steel cartridges cases instead of brass, but although some swear by them because they are a little bit cheaper, many people have had problems with it.
I bought my last ammo from SGAmmo.com, they have very competitive prices and shipping costs.
There are, like any other cartridge, other varieties of loadings with bullets lighter and heavier, pressures higher (Plus-P) and lower (mid-range match), lead bullets, soft- and hollow-point bullets, but they are all for specific uses, and older 1911's generally won't cycle them reliably without some tuning to spring weights, extractor tuning and feed ramp contouring and polishing. Ignore all that.
Standard pressure, 230 grain round nose full metal jacket, Ithaca 1911-A1.
Yeah, baby!