A friend and I would like to go to Amsterdam for a few days in October. I have a few questions... how many days should we go for to see everything that we MUST see? Any hotel recommendations? (preferably something cheap). Also, how is the weather in October? Thanks!

Try a guide book that has Amsterdam in X days and you can determine what you can / want to see.

My favorite hotel is the Owl Hotel. http://www.owl-hotel.nl/gb/
Less expenseive than most hotels in Amsterdam.

Great location with breakfast included.

We visited Amsterdam a few years ago. Arrived there in early October. The weather was beautiful. Then went to France and when we returned to Amsterdam two weeks later, the weather had turned rainy and cold.

We stayed in the Hotel Aalders, which is about 100 meters from both the Rijksmuseum and the Van Gogh Museum. It is also about 100 meters from a tram stop, with frequent trams into the city center. The hotel is a small family run hotel on a nice, quiet, residential street. Breakfast is included in the price. We would stay there again.

Amsterdam needs 3 or 4 days at least.

Hotel? How about a 4 or 5 star for about 100 dollars a night?
Go to TripAdvisor's Netherlands forum and look for the "Bidding on a 4 star..." and 5 star threads. Look at the latest posts as there are hundreds. You'll learn how to use Priceline's NYOP to get a great deal.

How much time you need depends on what you feel you must see. Go through a good guide book, allocate a couple bit sites a day and you can figure out how much time you need. We cant really make that determination for you!