There are really a lot of different reels you can use on ice rods to get the job done, but…
I really cannot stress enough, that most reels that come on a combo are there just there for decoration and to charge you 10 bucks that the reel isn’t even worth. Folks are better off buying the rod separately and purchasing a quality reel by spending at least $20 on the reel. Its only 10 or so more dollars than the combo, and you won’t have any of the associated headaches of going with the combo. This really true for just about any combo, whether it be for gills, perch or walleye.
A good quality ultra light reel can be used with the shorter walleye rods (24 to 28 inches), while some of the longer rods will/can take a larger reel due to their length and the balance between the two. Abu Garcia, Daiwa, Shimano, Tica, and even Pflueger all make some quality reels that will get the job done. You won’t need to go any higher than a 1000, 1500, or 2000 size in a Shimano or Daiwa, the Cetus from Tica is popular in the more expensive model, Pflueger Supreme and President and Abu has the 301 and 501.
Now, most of the reels I have at one time or another started out in the mid-40 price range (Cardinal 301 and Caprice 500 and 1000), and it will depend on the amount you want to spend. Ask a knowledgeable employee if you can find one at the place you shop and ask what the track record is of the reel you like if it is less than that. Even some of the more expensive reels are either junk, or just over priced. You should be able to find something that you like.
One of the best reels for outdoor walleye fishing, has been around the longest. The Daiwa SS 700 might look like a clunker, or really old fashioned, maybe not even fit the hype of so many ball bearings. But hands down, from the anglers who know, it is one of the first choices they would take. The reel just doesn’t freeze up in extreme cold weather, but the kicker for all that dependability is the price, just a bit under $90.00.