Blue square runs are the intermediate trails. Black diamond runs are for advanced and expert skiers. In order to improve, you have to ski. You may be ready to ski every weekend, but you will want to find a group to ski with. If you don't already have a group of friends that ski, check out a ski club.
Most cities have ski clubs that organize weekend trips.
To continue your progress, consider taking a ski class at least once a year. It's a good way to keep on top of your technique and build confidence. Your first equipment investment should be in ski boots. Rentals rarely fit right, they hurt your feet and hinder your skiing ability and enjoyment. Don't buy used boots.