Most smartwatches need an app to set them up, and you usually need the app to see long-term data. The watch typically only shows real-time data (starting from midnight) and maybe some basic trend data for the last 7 days. Also, the watch has a limit on how much data it can store, often around a month, before it starts to overwrite the old data (but you can’t access older data directly on the watch). For most cheaper watches, the data needs to be synced with an app to get processed on a server, which sends the data back to the app. This happens in many cheaper smartwatches too.
There are exceptions though, like Android wrist devices (which run a more basic version of Android and don’t sync with your phone). If you use a Garmin watch, you don’t have to use an app to set it up, but you won’t get access to extra features like notifications, weather updates, and calendar info. You can sync Garmin watches to your PC or Mac using Garmin Express, or even set them up directly on the watch itself (though it’s a bit of a pain). If it’s a Wi-Fi enabled music watch, you can sync it to Garmin’s servers, transfer data, and view it through the app. However, most of Garmin’s data is processed directly on the watch, so you can still use it, but some more detailed data might be missing unless synced through Wi-Fi.
With cheaper watches and some big brands like Huawei and Amazfit, you’re sending your data to China, unless the brand is one that doesn’t have any Chinese connections. While we hope they aren’t scraping your data, there’s no way to be 100% sure.
As for music controls, most watches can handle it, but they might not work great unless the app is good.
Steps? All of them should do that.
If you’re worried about wrist size, just measure your wrist with a piece of string and check the size against a ruler. Many brands list the wrist size in the specs (leave a couple of millimeters on each side).
Also, check out posts from u/EskeRahn, as they have a list of smaller and thinner watches. Most of the smaller ones are in the 40mm case range. The smallest is the Garmin Lily series unless you go with a fitness tracker, which could work for music control and steps.