Hi,
@aleem.k713.
@divinh gave you great advice.
I would suggest that you spend the entire time in Komodo and not do a Bali-Komodo crossing or similar...You will get to spend more time in the park. North and central are warmer than southern sites which have colder upwellings. Spring to fall (March-October ish) is usually higher season with Nov-Feb being lower season. Some boats continue to offer liveaboards during the lower season whereas other boats go elsewhere in Indonesia such as Raja Ampat or Banda.
Komodo can also be dived by land-based day boats. You can stay at a resort (Komodo Resort) or stay in Labuan Bajo proper and catch a day boat out every day for a few dives. The day boats will likely be cheaper but you will get convenience and flexibility on a liveaboard - you can time the dives better to avoid crowds or beat them to the sites. Your budget may dictate what you end up doing. There are very budget options available (shared dorm style rooms and bathrooms) with no AC and air only all the way to posh private rooms with ensuite bathrooms and AC and nitrox. Supply is quite plentiful in Komodo and my suggestion is to not spend too much on a liveaboard in this area given the competitive prices. You can get private ensuite bathrooms with AC, etc., without paying the upper end of the prices. I would suggest saving your money for a place where there are no other options given a lack of supply or remoteness of the region. I hope this makes sense.
As of right now, the Komodo park fee is about $110 but that is subject to change. That is not usually included in your liveaboard fee but payable on board. I would say a minimum of 4 full dive days is good, but 7 days is better.

Currents can be an issue here so getting a reputable dive shop with experienced DMs who are familiar with the dive sites, currents, and tides is really important. Otherwise, an enjoyable dive can turn into a nightmare.
If you are from NY, you may find it easiest to fly into DPS airport (Bali) or CGK airport (Jakarta). There are many flights from there out to Labuan Bajo, the gateway to Komodo. Many liveaboards book far ahead of time so I would move quickly.
PADI Travel is indeed a great place to check out availability and schedules and read more about each individual boat. They practically have 24 hour customer service and I have chatted them online at all times of the day and they are usually very quick to respond to give you advice or suggestions if you have any questions. They are very helpful.
I hope this helps!