...draw on in a 2D array on what SFML calls a texture, and then display that.
You should be able to draw directly to the window. At least, while drawing, then add it to the image when drawing (the current stroke) has been completed.
take in the current mouse position and continually draw in points while the button is held, but that feels like it's going to cause trouble in the long run.
Try taking mouse positions whenever the mouse moves, not continously, probably using events such as
MouseMoved.
Another problem I'm not finding an easy solution to is that points and lines and whatnot all seem to be set at 1 pixel width. It's not a problem I feel I need to be too concerned about since I'm just getting started in figuring this all out, but it does present a future issue.
This depends on how you decide to draw the final stroke. Your data will be a list of coordinates in sequence. You can draw just the 1px points, 1px lines between each pair, 1px spline curves based upon the coordinates, or you could draw a shape at each point, a rectangle between each pair (thick line), or interpolate the line/curve using multiple points and draw a(n) shape/point/image at each point, which can be spaced equally if required.
So I don't really know what I was expecting for an answer. I guess just verification that I'm on the right path or being pointed towards something that might help me out.
I suggest looking into
vertex arrays (use a vertex array for the current stroke i.e. while stroking) and doing it with just 1px
continuous lines to start with.