Planning to relocate to Budapest

Hi everyone. Nice to be on the forum and this is my first posting. I'm extremely interested in moving to Hungary and I'm not quite sure how to begin. I have visited Budapest and it seems like a good fit for me and it looks very affordable. I'm a USA citizen living in New York City right now.

Here are my questions: What type of visa do I need? I am self-employed and can work from anywhere.

How and where do I learn the language?

Where should I live? I like to have cheap rent and don't need luxury. Right now I rent a room without many amenities in NYC and I want to live on my own in Hungary.

I will be selling virtually all my belongings and keeping some clothes, my Kindle and iPod. I'm not bringing any books or furniture. I moved to NYC with two suitcases and plan to do the same to Hungary.

Any and all suggestions and pieces of advice are gratefully accepted! Thanks in advance.