Amsterdam has many hotels all over and all of them can get full on weekends that happen to be popular.
There is a good network of buses and trams in the city as well as the Metro for areas farther out.
Prices are not that much related to location. And the class of hotel may well have more to do with the price than the location.
If there are certain things you want to do or see in the city, look for a place to stay near to that. On the other hand, if you have not specific plans, the center of the city should be considered. That is all of the city within the tripple ring of canals (maybe with an exception of the 'Wallen' area, (the city wants to stop the use of the name Red Lights District,) not because it is dangerous but because it can become extremely busy with people who would not look out of the kids. The kids themselves will likely not be bothered, parents are often more upset.
Basically all of the city and several other cities near (if you can not find what you like in Amsterdam itself) will suit you, public transport is good and runs often. Most buses and trams in the center of the city are on 'every 5 minutes' schedules during the day, farther out at least every 30 minutes. Trains to Amsterdam from nearby cities typically run every 15 minutes.
Do not worry about the distances your kids need to walk, healthy kids who do play outside often can outwalk almost any adult.
The youth hostel, these days called Stay Okay, mentioned in the other answer may be a good idea for you. They do small dorms or family rooms, and families are welcome.
But check the location of the hostel you select, there is/used to be, a hostel in the Wallen area, but there is also one near Vondelpark, which always had good reviews.
As I live near enough to Amsterdam that I can go home every day I visit, I am not familiar with any of the hotels. Check reviews, as some places may not suit you.