Whether you prefer a couch to crash on or a mini castle, Airbnb has you covered. I have mostly stayed in airbnbs during my travels and prefer them to hotels, due to nightly rates typically being much more affordable. There are several filter options available, on the website, including the type of stay, property type, and amenities. You can also set the maximum price you would like to stay within per night. I typically book airbnbs with a washer/dryer and kitchen, since I do like to cook as much as I can when traveling. Additionally, airbnb also allows you to message hosts so you have any questions answered prior to booking.
TripAdvisor is the site I use when comparing prices across multiple accommodation providers. For example, for every listing, the price of that listing on Expedia, Priceline, Booking.com, and so forth, are listed, allowing for a quick comparison. There are some additional unique filters as well, such as filtering on accommodation within a certain distance of a specific point of attraction in the area. Another filter available is style, which allows you to select budget, mid-range, and/or luxury accommodation types.
Booking.com is the site I primarily use for booking hotels around the world. It has over 1 million listings in 200+ countries and has every hotel type available, from hostels to boutique hotels. It also will provide lists of accommodation based on the trip type you select as well.