me1, welcome to the forum.
Implicit in the order of investments is "...as far as IRS rules will allow."
In other words, the higher one's income now the more likely a traditional IRA will be better - but only if one gets to deduct that initial investment. Thus if you aren't eligible to deduct a traditional contribution, don't make one.
In your case, whether you should first maximize the traditional 401k or the Roth IRA depends on a few things, including
- the investments and their fees offered in the 401k, and
- your current and likely withdrawal marginal rates.
See the '401k vs Taxable' tab in the
case study spreadsheet - but the 401k fees would have to be terrible indeed to overcome the likely lower marginal withdrawal rate. In other words, from what is in your OP, "max the 401k first" is probably better for you.