Unless you buy the exact same string brand, style, and gauge, it's always good to give the bass a setup when you change strings. There's no direct translation from one string to another that'll guarantee not needing a setup. Different strings pull on the neck differently. Different strings sit on the saddle differently depending on how they're wound by the ball-end. Different strings intonate differently. Strings of the same gauge might have different core diameters; Slightly different alloy composition; core shape; etc etc. And that's just going rounds-to-rounds.
Very rarely will you every change strings to a different brand, style, or gauge and have them drop in without needing a slight adjustment somewhere. And if one thing needs to be adjusted, it's best to do the full setup in the proper order, otherwise you're building a straight house on a crooked foundation.
But don't let needing a setup dissuade you from trying different strings, though. It's really not a huge amount of work or alchemy to figure out. Once you're comfortable doing them it takes 15 to 20 minutes extra. And if you can't dial it in exactly perfect, you can always just take it to a tech to have it set up for you again.
Here's two fantastic & easy to follow bass setup guides by two guys who really know what they're talking about:
Pro tip 1: You can go through the steps with your bass right now as-is and just see how the measurements and intonation are. You know it's properly set up, so you can just check the steps along with the video without changing anything and you'll be able to see what's going on in there.
Pro tip 2: When adjusting the truss rod, loosen the strings, make a 1/8 or 1/4 turn adjustment, and then re-tune to check the adjustment; repeat as necessary. Don't try to adjust while under full tension, especially with flats on there. It's a few extra steps but it'll make your life much easier and much less likely to break anything or over-tighten the truss rod.
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As for which strings to pick, strings are eternally a matter a personal preference. If you ask which is best, everyone will just tell you their personal favorite in their favorite gauge and you'll have as many answers are there are options.
There's no right string beyond what you like the sound & feel of best on your bass. La Bella and Thomastik-Infeld are probably the two most common brands of Flats. I see D'addario chromes mentioned a lot on TB, but also i think they're a bit different sounding from most other flats. I'm a La Bella fanboy. But that's just me.
You best starting point might be just to figure out what flats your favorite players use on songs you love the tone of, and start from there.