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I naively originally thought the title's request would be too vague, considering the hundreds of different Android smart phones out there, but I'm having trouble finding one that comes rooted.
In case there are many phones to choose from, I'd go with a minimum of:
I don't actually need/care about the cell-phone part itself, nor the cameras.
Pre-rooted phones are a niche market. As a practical matter, I think you should settle for one that is easy to root.
One of the few phones to come rooted was Fairphone 1, but it isn't manufactured anymore and doesn't have Android updates after Lollipop. Fairphone 2 comes with a non-rooted OS by default, and has an official rooted OS image, but the official rooted image is not being updated. However, it is supported by LineageOS.
Fairphone is a fair trade phone: they strive to ensure that the whole manufacturing chain from mining to assembling respects decent labor standards (working conditions, pay, etc.). It's markedly more expensive (and also heavier at 168g) than other phones with similar performance. Buying a Fairphone is a social gesture, not a purely consumerist purchase. Fairphone documents the cost breakdown (first edition). On the upside, if some part breaks, you can order a spare: you won't get stuck with a battery molded in plastic!
Fairphone's attitude towards openness is somewhat ambiguous. They prioritize fair trade over software openness, so some components use proprietary drivers. However, they are sufficiently committed to openness to ensure that you will always get an unlocked bootloader.
I have a Fairphone 2 and I'm happy with it now. However, until someone managed to make a LineageOS build, the choice was between an obsolete rooted OS from Fairphone and the official non-rooted, up-to-date OS.
If the important thing is to have a phone that you're sure you can root, I feel the best advice is to get a Google flagship phone. These are designed to be development phones and so come with an unlocked bootloader, they have official OS updates longer than just about any other phone, and they tend to have good community support (through CyanogenMod and now LineageOS).
If it is okay for you to root the phone with very few easy steps as possible then mi's range of phones are the ones you must be looking for. MI does provide warranty for rooted devices in fact, there is an option in the security app to allow root permissions and sorta stuff and it is priced fairly compared to the Fair phone.
ALL you have to do is download a file which Mi offers on its website after registering yourself. Follow the instructions and boot into the boot loader of the device and install the zip file you downloaded and reboot your device to the normal state to enjoy your rooted phone
