Someone else can verify this too, but my thinking is this:
With a take home pay of around $122k, you're probably in the 25% or 28% tax bracket? It makes sense to me to go with a Traditional IRA and put away $11k per year. This way you get the tax benefit right away (~~ $2800/year saved). Then, because you are so young, you can later use a Roth conversion ladder to convert that money to a Roth, where it'll grow tax-free.
The next thing on the totem pole would be an HSA, which will let you contribute $6650 per year for a family. This is also deductible from your taxable income and not subject to FICA taxes.
Still after that, you can use a taxable account.
And down the road, it'd make sense to set up 529 plans for the mini mustaches!