There are 3 student-specific visas which you can apply for to study in the USA: F1, J1 and M1 visas.
This is by far the most common type of visa given to internationals looking to study in the USA. If you are on a full-time course then this is the one for you. In addition to studying, it also allows for on-campus, part-time work (fewer than 20 hrs/week) and has a strict expiration date by which you will have to have finished your studies.
Applying for a US visa can be tiresome process, but it’s necessary if you want to live somewhere as nice as Berkeley! When you make your application, you’ll have to provide the following:
An application fee for the process (non-refundable)
Your completed DS-160 form
A DS-157 form if you’re a male and between 16-45
You must also have proof of financial means (which will vary depending on where in the United States you’re studying) and have a formal offer from your American institution. Make sure to arrive no more than 30 days before your first class, and to leave again after no more than 60 days after your term ends, unless you change your visa in the intervening time.
These are both less common as they apply to more specific cases than the F1. The J1 visa is for students who wish to undertake practical training in the US which is not available in their home country. The M1 visa is for students attending a vocational or nonacademic school.
Opening a bank account in the US is really not all that complicated. To choose a bank, I’d contact the host university and ask for their advice - they’ll know who is the most convenient for international students in your area. When you call the bank to arrange an appointment, make sure you convince them that a face-to-face meeting is better than opening the account over the phone or online. Being an international means there will be more hiccups en route, so it’s easiest to work with a real person.
You will be required to provide the following documents:
Your personal details (name, address, phone number etc)
A valid passport
An I-94 card (the card you sign when entering the country)
Secondary ID (such as a driving licence)
Letter of enrolment from the university
Funds to deposit into the account
Getting a SIM card in the states is easy, as long as your phone is compatible. Some phones will not work in the US since the range of frequencies required by US devices and those in Europe are different. However, for most modern devices you should be okay; Google the name of your device and check if it is Tri Band or Quad Band - if it is either of these, you should be good to go!
Just shop around for the best deal from the big US providers (Verizon, AT&T, T-Mobile and so on) and make sure you get a decent amount of data.