Don't let anything get in your way of starting ASAP.
Vanguard is a popular institution for this. Call them and set up once-a-month automated deposits from your bank account. There is a yearly limit if you're under 50 of $6000. So send
them yourself $500 a month or as much as you can handle. Also FYI you may NOT be eligible for a Roth if your yearly income is above $124000 (or $196000 filing jointly).
Open an IRA online, and get help choosing the type of IRA and investments that are right for you.
investor.vanguard.com
Once your funds at the institution reach a certain amount (the minimum investment) you can put it into a mutual fund or some other investment vehicle. You should do some research to decide what's right for you, but for example here are some popular ones:
VTSMX
VFINX
VIGRX
VWELX
You've already paid taxes on this money and inside the Roth your gains are tax free.
Here is a more in-depth explanation of how taxes work.