Just tagging on here.
1. Max out your retirement, HSA, kid's college, etc. contributions before you pay extra on the house. If you pay off your house early, you removed $X$ from the compound interest growth over 20-30-40 years. That's where it hurts.
2. Just save - research the 401K vs Roth. There are advantages to each. Anyone who says no advantage to 401K is fooling themselves. Don't get too caught up, the govt didn't make it so you can really max out doing Roth - the advantage is that there are no required withdrawals and it is easier to pass to heirs.
There are limits to what you can invest in both - makes it easier to do the math yourself. I did the math and it didn't make much diff - we use 401K to stay in a lower tax bracket.
3. All things being equal, retirement is about how much you accumulate and how many "passive" income streams you can generate. If you spend all your money paying off stuff, you aren't investing any of it.
4. There are advantages to being debt-free too, if you so choose. I lean to the savings side. If got laid off, could pay my monthly obligations for years to come. Could also pay off my debts and still have $ left on the table.