An important note! You can buy a single ticket, a ticket for 3 rides, a ticket for a week, and so on (more details here). But if you buy a Budapest travelcard, the cost of all public transportation will be included in it. The Budapest card has other advantages too: free entry to some museums and discounts for visiting the thermal baths, shows, observation decks, and other attractions. If you are planning to visit several museums and use public transportation, getting this card will save you money.
There were 3 of us on the trip to Budapest and we rented an apartment on Airbnb. It turned out to be much cheaper than a hostel. It also had a kitchen and a separate bathroom which is another big advantage over a hostel. We paid €120 for a 4-person apartment for 4 nights. This amount was divided into equal parts, which means that each of us paid €40 (€10 per night). The apartment looked exactly how it looked in the photos on the site — it was very compact, but comfortable. As we understood, 2-level studios are a normal thing in Budapest.