here i usually start eliminating- where things can’t be. so for example the 8 in top left can’t start in the 1x1 square, because if it did the column next to it would not start with a 2 (if that makes sense). so a cross. and just continue crossing out what the 8 can’t start. also the five on the right can’t start in the first row. sometimes that helps to move ahead a little bit
While I am well past this one now, I usually first fill in the definite cells in each row and column, then figure out where to put X’s based on whether the row or column reaches the edge (example: if the 2 starts three cells away from the edge of a row, then that first cell is one that I can definitely X,) and then put X’s in the all-ones if there are any, and then piece it together. I don’t normally consider how one column affects the others like what you said. Good insight.