Getting started in the US
This is a simple to follow to do list for things that will help you to get started after arriving in the US. Many of the items are completely free and may be of tremendous help down the road.
Get a Social Security Number
If you are eligible to receive a Social Security Number (SSN), you should get one. Even if you are not working in the US, you can often apply for one if you say that you need it for your driving licence or state ID (see below). While an SSN is often requested when opening a bank account, it is not strictly required and many banks even allow you to open the account BEFORE you receive your SSN, which you then need to provide later on.
Open a Bank Account
You should open a no-fee bank accounts. If there is a local credit union or bank associated to your University, this might be good choice to get started.
Many large banks (PNC, Chase, Capital One, Discover etc.) run generous promotions, where you can receive up 50-400 USD for opening a new bank account. While the promotions are often advertised online, you can often print a coupon, so that you can even take advantage of the offer when opening it in a local branch, which is typically the only way to open the account for people new in the US. I would therefore recommend to only open an account with such big banks if you can take advantage of such an offer. Typically, these deals require you to open a premium account with a monthly fee that is waived if you have a sufficiently large monthly deposit (salary or similar) or you keep a sufficiently large balance. You should therefore make sure that you can meet these conditions to keep the account fee-free for the first few months, after which you can downgrade to a lower tier account with a lower threshold to keep the account fee-free.
Long term, I recommend to aim to have the following two main accounts:
Ally Bank. This account has no monthly fees, no deposit / minimal balance requirement, high interest rates, free checks and everything else you typically need for your banking needs. However, as you are typically verified online through your credit profile, your application will be denied (identification failed) if you apply for it online. Instead, you should wait until you have a credit report with 1-2 cards and your application should succeed.
Chase Total Checking. This account has no fees if you have at least 500 USD of monthly deposit or a minimal balance of 1500 USD in your account. The account is actually worse than Ally Bank, but it is very useful to have a banking relationship with Chase in order to apply for their credit cards. In particular, if you are new to the US, it can help if you apply through branch.
Open your first credit card(s)
There are many good reasons to open a credit card account as soon as you arrived in the US. It is often required for car rentals, allows you to build a credit history and as your credit score increases, you will be able to apply to higher tier cards with useful perks (1-5% cashback, bonus miles, airport lounge access, travel insurance and much more). You can read more about building credit in the US.
If you opened a new bank account at a local bank or credit union, you can check immediately if they offer some free credit card, so that you can get started. Some university credit unions offer reasonable credit (like 3000 USD) limits for university students or university employees, which would not be offered by regular banks (often start at only 500 USD). If you are not eligible for a regular credit account, ask if you could open a secured credit card, i.e., a card where you deposit 500 USD to get a credit limit of 500 USD.
A regular debit card (VISA or MASTERCARD) associated to your bank account is NOT a credit card, so you will not get a credit report and score if you only have such a card!
Sign up for free credit monitoring
A few months after opening your first credit card, your credit reports should have been updated and should now reflect your new accounts. You should now be able to open free online accounts to keep track of your credit reports. There are three credit bureaus, namely Transunion, Equifax and Experian. I particularly recommend the following services:
Sign up for Internet
If the internet is in your apartment is not included in the rent and you need to choose your own contract, you will typically not have many options. It is a bit surprising for a capitalist country as the US to have relatively little competition and most of the market is divided between Xfinity/Comcast and Spectrum/TimeWarner. You will probably know best how many Mbps you need, but in many situations it is best to choose the cheapest option, which often is a promotional rate (like 40 USD per month for 200 Mbps) for some limited amount of time (like 12 months), after which the price will jump up significantly. If you do not live alone, you could consider to have the next person sign up after one year to sneak up again a promotional rate. Alternatively, it is almost always possible to renegotiate the terms when the price jumps up by calling. This will typically not be as good as the rate for new customers, but significantly better than the "official rate".
Get a Phone Plan
There are many options to choose from and it is difficult to recommend a single best one:
Family plans. Many providers offer family plans where you get 2-5 phone numbers / SIM cards for a group of people, which is often much cheaper than the individual plan. You do not need to be part of a large family.
Pre paid plans. There are lots of reasonable plans with sufficient data (a few GB) und unlimited US calling / texting for 15-30 USD per month. Pre paid plans have often the advantage that you can pause the plan for a few months, while you are travelling abroad.
Google Fi. This is a great plan if you travel a lot because it also provides mobile internet worldwide at an affordable rate (10 USD per GB, as of writing).
Get a Google Voice Number
Getting a Google Voice Number is an absolute no-brainer, as it is completely free and provides a US phone number to receive calls and text messages for free for the rest of your life (or until Google goes out of business / phone numbers are not needed anymore). Oh, and you can make unlimited free calls to the US and to Canada from your phone/laptop whenever you are connected to internet/wifi.
This is particularly useful if you are ever travelling outside of the US and switch SIM card, as you will still receive messages / calls on your Google Voice Number. I recommend this particularly to people who leave the US and still need a US phone number on file with their banks / brokerage accounts / etc.
In fact, my Google Voice Number is the main number that I give out to other people, because I know that I can keep it (or even port it to a regular phone plan if needed). Any calls / text messages are forwarded to my current mobile number, so if I ever want to change my phone plan I do not need to deal with porting a number, I just change the forwarding to my new mobile number without any interruption. Of course, if you do not want to depend on Google in this way, this might not be for you, but I had excellent experiences with Google Voice for more than a decade.
Get a State ID or US Driving Licence
There are many good reasons to get local identification, so that you do not need to always carry your passport to prove your identity or age. Such identification is also useful when you need to identify yourself online, such as when opening a bank account.
Create a MINT account
It can be a challenge to keep an overview of your bank accounts, brokerage accounts and most importantly credit cards. Mint.com is a free service which you can give (read only) access to your accounts to generate a comprehensive overview of transactions, account balances and your monthly credit card bills. It will also send you alerts if certain balances drop below a threshold or if you get charged a fee (very useful!). To use the service you will need to provide your login information to your respective accounts, which are securely stored on Mint servers. Many banks provide a specific interface to only provide the relevant information without giving Mint account access. This can be an invaluable tool to manage a large number of bank accounts and credit cards, but already helps if you only have 1-2 accounts and 1-2 credit cards.
Open an Interactive Brokers Lite account
This is a free brokerage account available for anybody with a US address. In my opinion, it is an absolute no brainer to open this account, because it is completely free, allows international money transfers and is in my opinion by far the best product to invest long term on the stock market (for retirement etc.). You can read my detailed review here, where you should note (a) that the Interactive Brokers Lite account is only available when you open it with a US address and (b) that there is a current promotion where you receive an opening bonus of 1% of your cash deposit (up to 1000 USD).
Be aware of tax implications
If you still have a brokerage, bank or retirement accounts in your home country or outside of the US, you should be read this article on US Foreign Taxation about potential tax implications. Depending on your visa status (exempt individual or not), you may become a US resident for tax purposes, in which case you need to declare foreign accounts and investment income. Moreover, many foreign investment vehicles (such as ETFs) fall under the PFIC regulation, which may lead to additional punitive taxation in the US and should be avoided.