Welcome back!
Most of the things you are asking about are simply done online now, including tax, voting and changing your driver's licence, and all through the gov.uk website. I've found all of the services to be very quick lately (new licence arrived in two days, for instance, while it used to take weeks, and amazingly, I got road tax refund on Monday having sold my car the previous Friday).
As for the mobile SIM, it depends on how you use it. I go with 3 because their internet rates are super low, and their roaming rates in many other countries are superior to anyone else. But those are the things I use the most, so it'll come down to your needs.
Be sure to remember that the funny yellow boxes on the side of the road aren't decorations, they will take your photo and charge your for the privilege, and add nice points to your licence (if you go too fast).