What series watch
What Apple Watch series would you recommend, I want to go running and use Spotify without taking my phone
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If you want to be able to use the watch without your iPhone, you need a cellular model Apple Watch.
If you want to buy a brand new watch, that means Apple Watch SE (the least expensive model, but it doesn't offer Blood Oxygen or ECG, so for fitness, maybe not the best option), Apple Watch Series 8 and the most expensive and durable watch, especially for fitness, Apple Watch Ultra.
You can compare the models and features here --> Apple Watch - Compare Models - Apple