I also have a studio in my house with about 1500 sf of space. When I purchased larger pieces of equipment, I was always looking for multi-functionality. Here is a list of the pieces I own and would buy again if confronted with the same question:
Bowflex – This machine can easily be configured to resemble health club equipment. A great plus is that the resistance starts very, very light, making it very suitable for beginners, the deconditioned and rehab scenarios.
Total Gym Power Tower – This is my personal favorite. What I like the best is that you can do a lot of things on it that are impossible to do in a health club. It has a lot of accessories and can even be brought to the function of a Pilates Reformer.
Paramount Dual Axis Cable Tower – This is one of those cable machines with moving arms to the side. I like that each side has its own weight stack and that the arms move both horizontally and vertically making it extremely flexible. I also use this piece of equipment as a place for balancing exercises. I lower the arms to create a cage and thereby a very safe scenario for balance exercises, standing on a Bosu for example. This really builds confidence in people.
On the cardio side, I have a treadmill, an elliptical trainer and a recumbent bicycle. If I had to pick one, I would go with the elliptical trainer, then the treadmill. My bicycle is used rarely, and I would not buy it again.