You should open a Traditional IRA or Roth IRA with Vanguard. If you expect your retirement income taxes to be higher, go with the Roth IRA. If you expect your retirement income taxes to be lower, go with the Traditional IRA. You have a few more months to make your 2016 contribution of $5500, and the rest of the year to make your 2017 contribution of $5500. You can contribute $11000 today. Then with the money in your IRA bucket, purchase VTSAX, Vanguard's low cost total stock market index fund.
The important thing to remember about these tax exempt accounts with annual contribution limits is that if you don't take advantage of them now, the opportunity is lost forever. So act now, learn a bit more, then modify to suit your needs. "Lazy portfolios" and "Bogleheads" are good search terms to start your journey. You should also open a standard taxable brokerage account with Vanguard, because it seems like you have more money than the tax deferred accounts currently allow you to invest.
To your question, it's better to pay taxes on the income when you are in the lowest tax bracket, either because your last dollar earned falls in a lower bracket, or because you are resident in a state with lower income taxes.