we don’t know what they told you. But to answer your question, you can not work on an ED Visa. You would need to get a new type of visa that allows for a work permit, such as Non-B. Once you enter Thailand on that visa, then you can apply for work permit. Your job should walk you through this or get you an agent to help you.
The islands will be too “small town” I think, but Phuket is nice because it will have everything you need but not so chaotic if you live a few KM from the city center