Why worry about the intersections? Just add the next shape when possible and tie off the thread when it isn't possible to continue and you have to start with a new thread somewhere else.
But then again...... Don't listen to me. I'm well known for being quite relaxed when it comes to piecing and the word 'perfectionist' is not in my personal vocabulary book. I'm sure you'll get plenty of superb advice here on how to do it.
Saying that, I do make sure that I use a fine needle when over-sewing hexagons together, and I match the thread colour quite carefully to the background colour of the fabric, or - if that is difficult - I use a neutral medium grey. And I'm a little fussy about the thread I use. It has to be fine but fairly strong. My personal favourite is Masterpiece from Superior Threads for this sort of work.
But whatever you do, jump right in and have a go. You'll work out what suits you personally as you go along.
And, of course, we want pictures of the finished piece.
I have a box full of paper-pieced flowers (perfect project to take with you when travelling), but haven't use them yet. I did make a table runner though when I was about 11 or 12 years old. At the time I didn't know that there was such a thing as 'quilting', and I had never heard of 'English Paper Piecing'. My grandmother gave me some scraps of fabrics, showed me how to do it and then left me to it. The box with the scraps came out every time I was visiting and it was raining, so I couldn't play outside.