All great points from nysptsman. Depends on the type of fishing you're doing, what vehicle you are transporting the shelter with, how you are moving it on the ice (you, ATV or Sled) and your budget. I mostly jig for lakers and browns so I move every 10-15 minutes. For this style of fishing a 1 man flip over shelter is perfect. I use a Frabill Commando for this purpose. Holds all my gear and my heater and is EZ to pull around even in deep snow. When I'm fishing for Pike or Salmon and using tip ups, I use one of two different pop up hub style shelters, again from Frabill because we are staying put in one place. I'm usually with other guys too so I have two sizes depending on the group. Forget the anchors supplied with these shelters and go on ebay and buy 4 ice anchors used by ice climbers. They're a little more $$ but when they are placed, they will absolutely not pull out and they go in and out like butter! The hub style shelters are also very light and easily transported. Lastly, if I'm going with a friend and we are moving around, I have an Eskimo Pro-Fish 350 three man flip over but this shelter is a monster and is only used behind my ATV or Snowmobile. Don't skimp on quality. The inexpensive chair types look great but one outing in a stiff wind and you'll be replacing it pretty quickly. Last year I watched BC Shanty's chair shelter implode on Lake Otsego in 40 mph wind. If you're on a budget, a good compromise is a two man hub style (Frabill, Shappel, Eskimo, Clam, Cabelas, they're all good) and it will work in all scenarios whether running and gunning or tip ups. Get a jet sled to haul it and your gear and your in business. Just get the ice climber anchors and you can easily move and re-set the shelter. Trust me on this one, I've tried just about everything in 25 years on the ice and nothing beats these anchors!
Good luck- Mike