My husband and I will be spending a couple of nights in Amsterdam at the start and end of our Netherlands trip at the end of May/early June. I have two main conditions for a hotel: Around $300 per night, and ONE train or bus ride from/to the airport(no changes). Don't mind being away from downtown as long as we can get to things using transit.
The Owl hotel in Amsterdam fits your criteria for price and transport. There is a bus to the aiport about a block from the hotel. It is a short walk from the art museums. I am not sure if it has air conditioning or if that matters in late May/early June -- I was there in October.
My other suggestion might be to stay in Leiden which is about a 15 minute direct train ride to the aiport and about 35 minutes to Amsterdam. I stayed at the IBIS across from the train station in Leiden but there are also more upscale hotels nearby.
The 397 bus will take you directly from Schipol Airport (AMS) to Museumplein, a very convenient area with a good number of forum recommended hotels and great transit connections. We’ve stayed twice at the modest XO Hotel Van Gogh, across the street from the Van Gogh Museum and steps from the Museumplein bus/tram stops. The hotel is half hotel/half hostel. The hotel rooms are clean and comfortable and the only time you might notice it’s also a hostel is in the morning when sharing the breakfast room with traveling young people.
There are also dozens of hotels within walking distance of the central train station. Use a search engine like Booking.com that has a map view to help narrow down options. Depending on time of year and whether you're there over the weekend, $300US per night might be a challenge to find.
LOVED our stay in Leiden! Trained into Amsterdam for everything and we were glad to be out of the chaos and crowds in Leiden!
https://www.bestwesternamsterdam.nl/en/
Short bus to the train, 2 train stops to airport
tram 2 is around the corner from the hotel, into museum area and Vondelpark and then to Ams center
A few more options, there are some hotel, notably an Ibis, near Amsterdam Centrale. Did not check, but typically under 300, but anymore, it may not be depending on season and what events are going on in town,
There are a number of modern hotels and a few BnB type places near the Slotterdijk train station, on the rail line from Centrale to the airport. I have stayed at the Holiday Inn Express there a number of times, easy to get into central Amsterdam by train, bus, or tram. Also easy to get to Haarlem, Leiden, and other towns, as the station is much smaller than Centrale.
Then I would also suggest Leiden, easy to the airport, not too bad into Amsterdam.