As you can see, there are multiple issues, and it is much more confusing than it should be, but unfortunately there is no simple answer.
Well, your last question ("how can I be sure a used phone is unlocked") has a simple answer: you can't, until you actually check it. About ten years ago, a friend bought an "unlocked" phone, but when he got to Spain, it turned out it was locked. (He ran into the issue Andrew H mentioned - In the US, he was using a SIM from a carrier linked to the one the phone was locked to, so he thought the phone was unlocked when it really wasn't). Back then, there were phone unlocking shops all over, so he was able to get it unlocked in Spain, and then get his EBay seller to refund him the cost of the unlocking. Today, phone unlocking shops are rare, and you may or may not be able to get the problem fixed abroad.
So, if you do buy a used phone, it's important to check it with SIM cards from several different carriers, right away, while you can still get a refund for it.
Will you want to use this new smart phone in the US, and if so, with which carrier? Or, will you only want to use this phone in Europe? This will determine which model you should buy.
I want to emphasize Andrew H's point: different editions of "the same model" have different specs for different countries and carriers. I just bought a new Samsung Galaxy S9. There was a locked one sold by T-Mobile (my carrier) and two different editions sold by B&H Photo Video that were unlocked. However, ALL THREE had different specs. For instance, the T-Mobile one has some extra 4G LTE frequencies that both of the B&H ones are missing (you only need these for rural areas in the US). Of the B&H phones, one will work with Verizon and one will not. As I said, it's complicated.