Hungarian public transport is quite cheap and safe, usually clean, and well-organized. However you should take care of your bag in the inner city, especially in crowded places like markets, trams, subways and ruin bars.
There is a Hungarian saying: "The devil never sleeps."
Tickets are available from the ticket machine and the ticket offices too. Mostly you can pay by card and cash too at the automat.
there is possibility to buy ticket by online or a regular paper ticket as well
you can validate the single ticket and the online ticket before you use the vehicle
you can also validate your online ticket using NFC or QR code before you travel
you don't need to validate the day tickets and season tickets and the paper tickets
The Hungarian services for shared bikes is called MOL BUBI It's the green bikes, yeah.
It is possible to rent a bike for 30 minutes for 1,000 HUF per month currently in October 2023 and pay after you ride. I think it is also worth it to try if you want to discover the city in an alternative and free way.