Changing the hosting of my website

My hosting provider is trying to get me out of my current cheap plan, which is a continuation of a plan by one of the companies they acquired. Since they now even do not keep my PHP version up-to-date anymore, it gets pretty inconvenient. So I decided to take my business somewhere else and even found a local hosting provider.

The coming time, after our holidays, I will be moving my website to the new provider, so please bear with me if at some point in the process things break. I know I have a master’s degree in these things, but that does not guarantee I actually master the process