When asked this question at seminars or on the ice, I always try to help by matching a rod type to their particular type of fishing style. I always want to know if the person likes to sit inside a shelter to fish or if they are more of a stay out on the ice and run and gun fisher, as each spot lends a different answer to what someone should look for in their ice-duty walleye stick.
For inside work, length of the rod is of most importance, as you have to deal with confinement. Here, you are looking mainly at a rod in the 26” to 30” range to avoid hitting the rod tip on the shelter wall as you are jigging and setting the hook. Outside, you do not have to worry about this dilemma, and I would suggest using a rod a bit longer as it allows you to get away with larger guides on the rod and still stay balanced. I personally like a 38” rod for outside duty, but somewhere between the 34” to 38” range is what you should look into. Now, double duty, 30” seems to be the right size in most 2 man sized portable fish houses and 28” for the smaller one man houses.
For rod action, Medium action will be your overall best bet for almost all lure weights and water depths. Now, if your lures are going to exceed a half ounce, get a medium heavy to back-up your medium action rod.