There are LOTS of airports in Indonesia and they are quite easy to navigate. If you're travelling long distrances, check the flights as they are sometimes cheaper than busses and trains.
Lionair is one of the main budget carriers. I always recommend using Skyscanner or Google Flights first to check the prices. If you're booking a budget Lion Air flight, you can do it directly through the website: https://www.lionair.co.id/en/home