I have some edges that I want to merge, adding a vertices at the merge point…
what’s the best way to go about this? 
Choose the edge you’ve got marked in blue, and subdivide(W, S.) In the options change the number of cuts to match the edge your joining to(in this case it would be seven.) Then choose those edges, and the edges you’re joining to, and Bridge Edge Loops(W, E.) Then in the options tick the merge check box, and adjust the Merge Factor for where you want them to merge at.
In the image you show, that’s going to leave you with a big n-gon, and non-manifold geometry that will have to be cleaned up… but it’s all part of the game. 