I agree that you should buy a joystick as soon as you can. It will tranform your simming experience.... and "transform" is not strong enough to explain how much things will change for you

For the landing, I have a very simple trick: Look at the runway while you're still approaching. Try to "extend" it in your mind, make it, say, 3 or 4 times longer, make it a very long line, and then choose a point on this line that is far enough from the beginning of the runway, and just fly there, go to this point that you have chosen.
When you are more or less over this point, turn toward the runway. You may not be perfectly lined with it, but it should be ok, and at least you will still have plenty of time to correct your lining. If it's already too late, that means that the point on the line that you have chosen was still too close to the runway, so choose another point further away.
See ? The trick is simple: don't try to make your lining manoeuver too close to the runway. Give yourself more space and time, go "away" from the runway first, then take your time to line-up properly, without stress.