I'd second TweetTweet's recommendation. Buy Carol's bible.
You need a tax number in order to do most things, e.g. open a bank account, buy a car, rent a house/apartment (legally), buy a Greek phone/SIM etc, so that has to be high priority. Once you have a Greek tax number you have to fill in a Greek tax return each year. When you get the tax number you have to be registered either as tax resident or non-tax resident. Tax resident means you have to declare your worldwide income and pay tax on it in Greece. Most people try to remain non-resident. If you are non-resident you have to have a Greek representative and all correspondence will go to that representative, not to your own address. I would say the first step, therefore, is to get a good accountant well versed in ex-pat tax affairs, use them as the representative and get them to help you get the tax number to ensure you get it right. Get it wrong and you could finish up in deep doggy doos.
Be aware that there are still strict capital controls in Greece so it isn't particularly easy to open a bank account. I've not tried recently but I have been told that you have to deposit at lest €10,000. They don't want Greeks opening multiple accounts to get round the withdrawal restrictions. They will also want lots of documentation.
I am not sure if it still applies but I think if you buy certain items, e.g. a house, a car, a boat etc, you will need to prove where the money came from and the tax office will only accept a certificate from the Greek bank that you transferred money into from abroad. Simply arriving with a bag of cash and depositing it may not be a good idea. The accountant will advise you.
To get a residence certificate you need to prove that you have income, healthcare and somewhere to live so you will need to rent somewhere, preferably with a legal contract drawn up on the official form and registered with the tax office, before applying. You don't need one for most things but buying a car is potentially easier if you have one.
No need to change your driving licence provided you have a relative/friend in the UK who you trust and who is prepared to let you use their address. Most people I know keep a UK driving licence. That might be affected by Brexit. The EU regulations allow you to drive on any EU licence but once the UK leaves the EU the UK licence will no longer be an EU licence. What happens then is anybody's guess.