What would I have to do to remove partial panelling and put up new dry wall? could I do it myself?

You should be able to drywall right over everything. Get some drywall nails, or screws, drywall tape, and drywall mud. I would recommend 1/2 drywall. It may cost a little more but you will come out with a much smoother wall. If you get thin drywall many unknown bows in the wall may be seen, should anything be out of square. With 1/2-5/8, you should get good straight, smooth walls. Your walls will also be stronger. If you have weak spots in your paneling, thinner drywall will not offer much support or strenght in those areas.