I'd like to open my first Roth IRA
However, I'm not sure which broker (or mutual fund company) to open it with.
What are the characteristics/statistics I should be looking for when picking a broker (or mutual fund company)?
Are some companies better than others? (If so, in what way?)
...Does it even matter??
My main criterion for choosing a broker is the fee schedule. I care about investing in index funds and paying as little as possible in fees.
In the US that brings everyone to Vanguard or Fidelity, and currently Vanguard edges Fidelity out on costs for the particular funds I am invested in.
If you don't know how to evaluate funds and are looking for someone to help you make good investment decisions, then you want a financial advisor. My suggestion is to look for one that 1) doesn't try to sell you insurance first (since insurance is an expense, not an investment), 2) can explain to you the the relationship between risk and return (and what mix is right for you) and 3) recommends funds that have good demonstrated returns after fees have been removed.
If you plan to pick your own funds and just want a transaction broker, go with one of the free/cheap online discount brokers. Many let you invest in hundreds of different funds, so look for brokers with the cheapest fees.
The most important thing is to keep in mind the deadline. If you want to have it count for 2016, you need to open the account and transfer the funds by tax day. Don't wait until the last day to do it, or you could run out of time. Setting up the initial account, and them verifying your information and transferring the money could take a few days.
First decide how much of a lump sum you want to invest initially. This will determine some of your options because the mutual fund will have a minimum initial investment. Many of the funds will allow subsequent investments to be smaller.
The beauty of a IRA or Roth IRA is that if the fund you want is out of reach for this initial investment in a few years you can transfer the money into another fund or even another fund family without having to worry about tax issues.
Now decide on your risk level and you time horizon. Because you said you are student and you want a Roth IRA, it is assumed that you will not need this money for 4+ decades; so you can and should be willing to be a little more risky.
As NathanL said an index fund is a great idea. Many also advise an aged based fund. My kids found that when they made their initial investments the age based funds were the only one with a low enough initial investment for their first few years.
Then pick a fund family based on the general low fees, and a large mix of options.
The best thing is that in a few years as you have more money and more options, you can adjust your choices.
