What would you consider an appropriate distance for a beginner? 2K perhaps?

Personally, I think it's all down to the individual. Don't go out for a set distance. Run as far as you can at a comfortable pace and that's your beginners distance, it'll be different for everyone. Next time, aim to beat it.

Fartleking is a mind game you can play where you aim for say a lamp post or set of traffic lights in the distance and you speed up until you get to them then slow down again. Doing this at regular intervals when you get more into it will get you further faster without really realising it and you'll start setting personal goals easier.

Don't do too much too soon or you'll get shin splints.

i use sefton park which is a 2.5 mile circuit but on my very first session i did run for 1 minute then walk for 5 all the way round. I stayed to the same distance for ages until i was able to do the whole 2.5 miles in one go (which took about 4 months, going once a week). I then just varied the distance and / or varied whether i ran all the way or walked part of it