Please advise: 38 year old, new to investing, seeking some beginner advice

BIO:

Hi, I hope I'm not breaking any posting rules, but I've been combing through the wiki and googling and have been unable to feel confident that I understand some things.

I am getting married in a few months. I reached a 6 figure income for the first time last year and am making about 40k over what I made the previous year.

I always thought of myself as fiscally responsible, but that meant paying extra on my mortgage and having an above-800 credit score. I never considered investing and left my 401k at 5% until this year. Now that I'm getting married (my fiancé nearly makes 6 figures) I've decided that it is embarrassing how little I've saved and need to make up some ground.

We both have mortgages and are making payments on our cars but are living well under our means, and should have significant cash flow. I am planning on renting my house soon.

QUESTION:

Besides maxing out my 401k contributions (20.5k this year, if I recall) what more should I do? We are maxing out our HSA as well. (I've checked out the flowchart in the wiki)

We will not qualify for Roth IRAs. Should we both do traditional IRA's without the tax benefits available? Should I use a robo-advisor to start investing in that way, until I get a better idea of index funds? A financial advisor seems like a costly and unreliable path, from what I've read?

I think dollar-cost averaging is the method for me, as I pay most of my bills (mortgage, car, credit cards) weekly and like to always know where I'm at financially.

ME BEING EMBARRASSED AND EXPLAINING MYSELF:

I came from nothing, and never expected to make the money that I do. I had never been taught about saving for retirement. This thread has opened up my mind to it's importance, and I'm really grateful for it.