I am trying to get a feel and figure out for the best and quickest way to learn German for an absolute beginner? I have the option of group or 1:1 lessons – comments/ preferences/experiences please?

As a German teacher I'd say: principally, both options work.
The quickest way to learn German or any language for that matter is to be consistent and persistent - Keep at it and don't let yourself be put off.
With one-to-one lessons it's always a matter of whether you get along well with the tutor or teacher since it's a delicate thing. You do advance pretty fast this way, as the teacher knows exactly what to cater for.
On the other hand, being in a group helps, because of the "we are in the same boat" aspect and thus you do support each other. Plus, it's usually fun!

Either way, you are fine.

Again as a teacher, I'd say 'both'. It is much more fun to learn as part of a group- with a variety of partners to practice conversations with. But also have a private lesson from time to time to get the opportunity to focus specifically on any difficulty YOU have. I'd say the same for most subjects, including say, skiing.

Main thing is to try and immerse yourself as much as possible. Your head will literally hurt for a while, but then it will all click into place.

Try to steer clear of ex-pats and forums as much as you possibly can- it really does help.

From the student side, having tried both, I must admit I always enjoyed the group lessons more. In the 1:1 situation I felt far too self conscious and kind of stupid - at least with others there I felt like I wasn't alone in my stupidity (and realised that actually I was quite good compared to some of the others ).

Even though the teacher was very nice I just didn't enjoy the 1:1 situation. I imagine it depends on you as much as the teacher, but why not try both and see which you prefer?

The most important part for me was being able to practice outside of classes, because my work was in English and pretty much everyone I knew spoke English. For that I'd highly recommend enrolling in some kind of other practical adult education class - like cookery or painting or DIY, to give you a chance to just hear the language being spoken in a normal setting outside of German class. Make it something where you can follow by copying - so not German literature or something, but anything where there will be practical work as well as listening. I learnt to drive here which did wonders for my German! Also, watch German TV as much as you can stand - start with something like the news (where they generally speak clearly!) or sports programs if you're into football or something.