Rick's recommended hotels are always going to fill up well in advance given how many people buy his guides. His picks aren't the only options in town and if you do your research and carefully check reviews to see what the common views are on location, noise levels, cleanliness, etc., you should be able to find something (albeit basic and on the small side) in your price range. Central Amsterdam is pretty compact and easily walkable. If you stay further out thinking it's the best way to save money, don't forget to factor in the additional costs for having to take public transit regularly. Sometimes the extra cost and time spent in transit makes any "savings" a wash in the end and the time lost in transit could have been avoided by increasing your budget a bit more so you can be more central and walk more.
The Ibis Styles hotel that is a couple of blocks from the Albert Cuyp Market, Heineken Experience and about 1km to the Rijksmuseum has rates starting around 89 Euro/night. Cocomama, located in the De Pijp area, is a boutique hostel with private doubles that are in the 100 Euro/night range. CitizenM hotel near Beatrix Park may also be an option.
I would also recommend doing a search via Booking.com or Airbnb in your price range to see who has availability. Sometimes if you are willing to lock in on a non-refundable price, you can get closer to what you are willing to pay. You just need to be 100% confident of your travel plans if you go that route.
The only area I would actively avoid in the interest of getting a quiet night's sleep would be anything near Centraal, the Red Light District or in the immediate vicinity of Leidseplein where all the bars and restaurants are concentrated. I stayed at Hotel D'Amsterdam which I found a great rate on through Booking.com and even though it was just a 3 minute walk to Leidseplein, it was on a very quiet, mostly residential street but the hotel was very convenient to the museums, Vondelpark and the bus to/from the airport.
From a cost perspective only, the city bus is cheaper. However, "better value" between bus or train to/from airport really depends more on convenience and where you end up staying. I've stayed over near the Nine Streets area and found it easier to take the train to Centraal from that location, but when I stayed at Hotel D'Amsterdam, it was easier to take the bus with my luggage. The train ride is shorter (city bus takes about 50 mins from Leidseplein), but if you have to transfer to a tram to get to or from the train station, then factor in that additional time and hassle of lugging your bags around to see if it is worth it. There are also coach buses that run to the airport, but the price is nowhere near as cheap as the city bus.
