The flight should finish at SAI, not at a loose connection
Flights now land at Siem Reap Angkor International Airport, SAI. The old airport could not keep up with the traffic and has closed; its replacement sits east of Siem Reap.
From the United States, you cannot fly nonstop into SAI. You connect through an Asian hub. Bangkok and Singapore are among the places with flights into the airport; Kuala Lumpur is another. A flight search that ends at a hub has not yet delivered you to Siem Reap.
I would try to keep the trip through to SAI on the same ticket. Buying the long-haul flight and then assembling an onward booking separately may look neat in the search results, but it gives you another connection to manage before you even reach Cambodia. The separate reservation has no interest in how good the original deal looked.

Pick the ride by where it actually leaves you
For the official airport bus, follow the Airport Bus sign after leaving arrivals. The counter is on the left. You do not need to book ahead; you can wait for a departure. At the other end, though, the bus finishes at its own station in Siem Reap, not at your hotel. A tuk-tuk can handle the last stretch, but don’t count on one at SAI itself: it may not be allowed to pick up there. Different location, different job.

The post-office shuttle uses a different drop-off: the Siem Reap post office by the river. It is another station-to-station service, so check whether that location works for your accommodation.
Shared hotel transport does a different job. Book the minibus in advance, meet the driver at the exit, and let it take passengers to their hotels. Other travelers have different addresses, so you do not control the order of the stops. It suits anyone in no hurry.
A private car or minivan is yours alone. You can arrange it at the airport or book ahead. Departures into Siem Reap thin out late in the evening, so landing late with friends, I’d book the car before flying.
The return trip starts at a different address
The airport bus leaves from its station in Siem Reap. The post-office shuttle starts at the post office. Neither route automatically picks you up at your hotel.

Book a seat a day ahead for the return, or ask your hotel to arrange a car. Allow generous room for the drive out. I would rather have the departure transport settled than spend the last evening deciding how to reach an airport outside the city.
At SAI, international departures use the upper floor and domestic departures use the ground floor.
The visa and arrival card are different jobs
US citizens need a visa to enter Cambodia. A tourist can request an e-visa at evisa.gov.kh before traveling, or obtain a visa on arrival at the airport. For the arrival option, bring cash in US dollars.
Your passport needs at least six months of validity and a blank page. Keep an onward or return ticket available as well.
Cambodia also requires an e-Arrival card. Fill in the free form at arrival.gov.kh in the week before the flight and keep the QR code for passport control. It replaces the paper arrival, customs, and health forms, but it does not replace the visa. An airline may ask to see it at check-in.
Angkor is not going anywhere. There is no prize for landing at SAI and proving you can improvise a ride from the countryside. I would rather arrive knowing exactly how I am getting to the room.