The first thing to check is whether your phone is compatible with the smartwatch you want. You can't use an Apple Watch with an Android phone, as all the functions of watchOS require iOS to interface with.
You can use a Fitbit or Google Pixel Watch with an iPhone, but without Android or Google accounts, your experience will be sorely diminished. Samsung and Huawei also require handset-watch synergy to operate at their best.
However, many devices like Garmin watches and the CMF Watch Pro by Nothing require nothing more than their own apps to work, meaning you can use them with either handset just fine.