Should I go over certain lines with an engine?
If you want to, sure.
Just realize that their evals are not very accurate in the opening. I'll look at my opening lines with an engine but very rarely do I use the engine to outright reject (or accept) lines. You have to be careful.
Mostly I like to do it because my opponents might be doing it also, and I don't want to be surprised if they deviate using an engine suggestion.
Ultimately at your level (and my level too) it's probably not a good use of time though.
Do I use a specific chess opening website?
I don't know what's out there. Maybe there's something good... but openings are low effort high reward. Even if it's a repertoire put together by a strong GM, they can easily do a database dump, or give terrible suggestions, and then sell it for $20, and they can be sure amateurs will buy it, because low rated players are obsessed with openings.
In general I'd be suspicious of websites.
Do I read books? If so, what kind?
Personally I don't prefer repertoire books. I like to use databases and do it myself, this has its own drawbacks, but anyway...
As with any chess book read reviews. Ask around. Try to get something well regarded by the community. Like my comment about websites, opening books can be a quick pay day for a titled player.
What counts as too old for an opening book?
If you're playing teenage IMs and GMs you shouldn't waste time with anything but the latest books.
But since you're 1400...
The goal should be to have 5 to 10 moves memorized plus (and this is important) know the basic middlegame idea. What area of the board do white and black typically play on (kingside, center queenside) and how (broadly speaking pawns or pieces) and know the main pawn breaks.
Outdated theory tends to get you into trouble later in the game, where players are still in their preparation on move 15, 20, 30. Even if you bothered memorizing that much (please don't) none of your opponents will know enough for you to ever reach those positions.
( I'm not clueless about openings, as I have been playing chess for about 6 years. )
After procrastinating all my life, I'm falling behind.
Should I go over certain lines with an engine? Do I use a specific chess opening website? Do I read books? If so, what kind? I have many of these 'guide' type books and while they're useful to understand key concepts, there are many variations which they say 'you need to learn the full theory' (or something along those lines). What counts as too old for an opening book?
Thanks