Fascinated by this series of vehicles some time ago, I conducted a lot of research, and compiled some handy reference notes. This helped me put makes, models and production into perspective, and gave me a hand when trying to determine which LVTs could make an appearance in which battles (Pacific theater only). So for those who like such information ... here you go!
LVT Summary
LVT-1
Built: 1,225 (72 1941, 851 1942, 302 1943)
540 USMC, 485 US Army, 200 Allies
First used on Guadalcanal (Aug 1942) but only to ferry supplies
Also used on Bougainville (Nov 1943), Tarawa (Nov 1943) and New Britain (Dec 1943)
LVT-2
Built: 2,962 (1540 1943, 1422 1944)
1355 USMC, 1507 US Army, 100 Allies
First used on Tarawa (Nov 1943)
Also used on New Britain (Dec 1943), Kwajalein (Feb 1944), Eniwetok (Feb 1944), Saipan (Jun 1944),
Guam (Jul 1944), Tinian (Jul 1944), Peleliu (Sep 1944), Iwo Jima (Feb 1945) and Okinawa (Apr 1945)
LVT-3
Built: 2,964 (1 1943, 733 1944, 2230 1945)
All assigned to USMC
First (and only) use on Okinawa (Apr 1945)
LVT-4
Built: 8,351 (11 1943, 4980 1944, 3360 1945)
1765 USMC, 6086 US Army, 500 Allies
First use on Saipan (Jun 1944)
Also used on Guam (Jul 1944), Tinian (Jul 1944), Peleliu (Sep 1944), Philippines (Oct 1944),
Iwo Jima (Feb 1945) and Okinawa (Apr 1945)
LVT (A)-1
Built: 510 (3 1942, 288 1944, 219 1945)
182 USMC, 328 US Army
First used on Kwajalein (Feb 1944).
Also used on Eniwetok (Feb 1944), Saipan (Jun 1944), Guam (Jul 1944), Tinian (Jul 1944),
Peleliu (Sep 1944) and Okinawa (Apr 1945)
LVT (A)-2
Built: 450 (200 1943, 250 1944)
All assigned to US Army
First used on New Britain (Dec 1943).
Also used on Kwajalein (Feb 1944), Iwo Jima (Feb 1945) and Okinawa (Apr 1945)
In addition to the 450 built as LVT (A)-2, over 1,000 of the LVT-2s listed above (those built starting in March 1944) were assembled using the armoured cab specifications, giving them an appearance very similar to the LVT (A)-2 ... but these LVTs were not given the official LVT (A)-2 designation.
LVT (A)-4
Built: 1,890 (1489 1944, 401 1945)
533 USMC, 1307 US Army, 50 Allies
First used on Saipan (Jun 1944).
Also used on Guam (Jul 1944), Tinian (Jul 1944), Peleliu (Sep 1944), Iwo Jima (Feb 1945), and
Okinawa (Apr 1945)
So as far as LVT usage in the Pacific is concerned, the LVT-1 and LVT-2 "own" the Pacific theater for all of 1942 and all of 1943, and a good portion of 1944 and 1945 battles (in 12 listed above). Some of the 1944 and 1945 battles involved converted LVT-2s which became LVT (A)-2s in all but name. The LVT-4 comes into service in battles from mid-1944 onward (in 7 listed above).
LVT (A) usage is spread about more evenly. LVT (A)-1 appears in 6 major landings in 1944, and 1 in 1945. The LVT (A)-2 only appears in 1 late 1943 landing, 1 1944 landing, and 2 in 1945. Keep in mind some of the LVT-2 battles listed above featured vehicles converted into LVT (A)-2s in all but name. The LVT (A)-4 saw action in 4 landings in 1944, and 2 in 1945.
Hope this information proves useful!