Max out all pre-tax accounts. You should each be able to put the full amount into Traditional IRAs in addition to 401ks. That's $5500 each.
Open a Vanguard Traditional IRA (the one for you and the one for her will need to be under different logins, I think) and a Vanguard taxable account (assuming you like Vanguard). If you're sure you'll get the full IRA deduction (you should, at least, but maybe not her), then fill up the IRA before putting money in the taxable account. At some set time interval, transfer the excess money out of your checking account and into Vanguard.
If you're unsure about whether your wife will exceed the income threshold for reducing IRA deductions (e.g., she could get a bonus), then just make a partial contribution as early as possible and make sure you have the cash to top off her IRA come early next year, once you know her income for the year.
You can set up the accounts and transfer money in without knowing an asset allocation (the money can start in a settlement fund, which is usually a money market fund), but you'll need to decide on an asset allocation at some point. The Boglehead wiki is useful for that. You could keep it simple and do a
three-fund portfolio. Pay attention to
tax efficiency and put all bond and/or real estate, etc., funds in the 401k or IRA accounts. Pay attention to the fees between your 401k and IRA accounts when choosing where to put money. As you make more deposits, try to maintain your asset allocation.
You can invest in ETFs or mutual funds from within the same Vanguard account (Vanguard recently merged brokerage and mutual fund accounts). If you buy and hold a significant amount of money, it doesn't really matter which one you do.
Don't let the details slow you down. Opening the accounts and putting all the money into a total stock index would not be a bad decision. You can figure out asset allocation and tax efficiency and slowly shift toward that with new deposits later.