Tupperware makes a small, reasonably water-tight container that works well. The main advantage of the Tupperware container is that a stand clip is made specifically to fit it. The small, metal cup holder clips onto a standard Manhasset-style music stand and holds the water cup off the floor. Many catalogs and music stores often consider this an oboe supply, so it may not be listed in the section with clarinet accessories. While it's unusual to carry a stand shelf around, it is a very convenient item to use at home with a Manhasset-style music stand.
Pegs come in a wide variety of styles.
In general, the heavier, larger ones make for the safest stands, They are also the least convenient to carry around. In recent years, light-weight plastic pegs have become available. It's three legs fold up for compact storage. When extended they provide reasonable stability, even on carpeting. It folds up small enough to store inside the clarinet's bell in any standard case.