Which privacy first smartphones would people recommend for US users

If you want to run GrapheneOS, then you can only use a Google Pixel.

If you want to run Calyx, you can use any phone on the CalyxOS "Devices" list, which includes Pixels, Fairphone, and some Motorola phones too.

I personally recommend Pixels because they tend to get the fastest and longest-lasting OEM-provided security patches (e.g. the Pixel 8 and later get 7 years of updates from when they were released) and Android releases, and they actually have a pretty decent selection of self-repair kits available for if you need to do a repair yourself, or if you want a repair technician to not have to go through a complicated ordering process for spare parts.

how does it work putting it on a network?

Make sure to buy one that's not locked to a carrier, otherwise you'll be unable to install the custom OS in the first place, since the bootloader will be locked. You can still set it up with any carrier you want once it's unlocked. (this essentially means you need to buy the phone directly from the manufacturer. Don't buy through your phone plan, or through a trade-in/upgrade with your carrier)

Your carrier, once you request it, will either mail you a physical SIM card you can put in your phone, or a digital eSIM you can activate immediately. I prefer eSIMs for convenience, but it's entirely up to you. (you can check out this list of pros and cons if you're interested. They're mostly negligible.)

Do they go on the regular networks like at&t, sprint, Verizon etc?

Yes.

Now, if you're going to install a custom OS, definitely make sure you watch a couple videos and read the official guide for the OS you choose on how to install it. You definitely want to make sure you don't screw it up.

For example, if you're installing GrapheneOS, you might want to use a chromium-based browser (chrome, ungoogled chromium, brave, etc) over something like Firefox, because it sometimes has issues installing via the WebUSB installer, while having no issues with chromium based browsers.

These little details are something you'll want to pick up from those resources so you can actually feel confident when you flash the OS to your phone, and make sure you do it correctly. Plus, you get the upside of knowing more about how exactly the OS protects you compared to stock android.

I personally recommend GrapheneOS if you're good with using a Pixel, since it seems to have some of the strongest security guarantees on top of its methodology around privacy. (Google has very strong hardware security measures that other phones don't always have, which GrapheneOS takes full advantage of)