Just to add to Iain's advice above. It's very much a risk/reward issue what shots to play. If I was bowling, aiming to bowl an inswinger then the batsman has opportunities against the ball that doesn't swing or doesn't swing enough, as you have to start it outside off to get bowled/LBW. The straight or cover drive are scoring areas IF you watch the ball carefully and don't push at the ball, exposing a gate in the process. Most legside shots are safe as long as you don't over balance.
The flipside is bowling an outswinger, I'm looking for the outside edge or even possibly off stump if the batsman plays across the line. I have to start it around middle and look for the angle and swing. This means the cover drive is a very dangerous shot to play as you might be using an open face + a balls path arcing away from you, equals big trouble. Likewise if I push it more leg stump, you could get a leading edge. As Iain says, you have to be very careful playing to leg. However, play straight and it's an opportunity to pick off the outswinger through the legside or straight down the ground if it doesn't move much.
Another thought on short balls, it might be worth looking at the bowlers action. Many left arm overs basically push it across you. They are open chest or the arm/back goes beyond vertical. The stock ball will always go across you and staying legside of the ball might be a first option. A more classical side-on left armer would get it to straighten back in or hold it's line. Getting inside the line would be the first option. Whatever you do, have a look at his setup first and have a think about what he is trying to do.