In most cases you'll want the low-starch "waxy" potatoes for your salad. They keep their shape even after boiling. They are often referred to as "new", have thin skins, and may be red or tan or even purple, which make a great looking salad.
You can also try starchy baking potatoes - like Idaho or russets. The breakdown of their starches will give your salad a little creaminess. In addition, their mealy texture is not a bad attribute in salad.
Yukon Gold, the so-called all-purpose potato, will give you a firm potato whose exterior will deteriorate just a little adding some creamy texture and still hold their form. You might even consider mixing the potato varieties but cooking times may vary. Enjoy!