I know every kid and situation is different, but ours were 12 and 14 the first time they went off on their own in a Disney park and they just used their regular phones. Maybe it helped that mine had phones for a number of years before this trip and had proven that they can be trusted to not lose said phones. We already were using Life360, but it was really kind of funny using it at WDW. I could be having a drink in the UK and see that my kids are in line for Spaceship Earth. They're both iPhones, so I could also use the FindMy feature to alert them if they missed a text or call from us. I know most of the major phone makers have some kind of find my style feature, which could help put your mind at ease if losing a phone is your concern.
If you're not comfortable having them take their standard phones, you could get Tracphones. Ours started with those back in elementary school, when they started riding their bikes to and from school while we were in the office at work. We opted for smart Tracphones vs. flip because I could add the Life360 app for tracking. Amazon usually has nice deals on these that come with a decent allotment of minutes/data. It's been several years, but I think I spent about $35 and got a smart Tracphone with triple minutes.