Regarding the watch face, as long as you can change the watch face or use third-party options, this shouldn’t be a big issue. Smartwatches are usually bigger than traditional ones, so the screen and face will likely be larger. If you use a lot of menus, you might want to look for a watch where you can adjust the system font size, like the Apple Watch, Wear OS, and Garmin (not sure who else offers this). I find this super helpful as my eyes aren’t as sharp anymore.
For the timer, I’m not sure if I fully get the 30s, 1min example, but many smartwatches now have interval-based features. These are common on fitness brands like Garmin, Coros, Polar, and Suunto. If you choose an Apple Watch or Wear OS watch, there should be apps for this too, and most of them have timer functions built in.
As for vibrations on notifications, they all do that.
As for style, it’s really personal. I suggest you focus on the features first and then choose one that fits your taste. You might also want to consider hybrid watches (like Withings, Garmin Vivomove, or Garmin Crossover) depending on what activities you want to track.
About the cardio sensor—assuming you mean a heart rate sensor, the best one for you depends on what kind of activities you do. For some activities, a chest strap is the only way to get accurate readings, and not all smartwatches can connect to one. But for steady activities, most major brands will work fine, like Apple Watch, Pixel Watch (Wear OS), Samsung Galaxy Watch Ultra, Garmin, Coros, Polar, Suunto, Huawei, some Fitbit models, and even Amazfit (though that’s model-dependent).