Few things that might help I think is to tell you what I used when I first started.
One of the most important pieces of equipment you can have is an ice "bar" also known as an ice chisel, eskimo makes a great one for cheap under 20 bucks, or you can just flat get a long piece of 1/2 emt conduit and put a little lead in it. I use mine to familiarize myself with "safe" ice sounds, safe ice should sound like a solid mass, no hollow sounds, more of a "BUNK" than a "THUD". Plus if it's long enough and you go through to use it as a brace bar to work yourself up again. I've had to do this a couple of times in marshy areas when a leg or two goes through a soft spot I didn't recognize.
On that same note I would recommend some ice picks, you can get these really cheap and good quality, I have a pair with telephone cording type stuff between the two that stick together and go around my neck, i've never went in over my head "knocks on wood" but I wear them each and every time I get on the ice, even if I know it's good ice.
Also some cleats might be good, eagle claw makes em cheap 5 bucks or so, then go in the middle of your boot so if you do start sliding around you can get some grip. The full foot cleats are better but they are more expensive, the mid boot cleats seem to make a guy do the splits from time to time, luckily for me i've grown into my bibs enough to make movement pretty difficult
5" Mora hand auger , 5" sounds crazy but I never had a problem with the diameter fishing on Wisconsin lakes, I've pulled 30+" fish out of 5" holes. Granted bigger is better within reason. If you don't want to shell out the money for a power auger I suggest not going above 7" I got a 7 awhile ago and used it for two seasons then bought an 8" Eskimo power auger. It's the smaller engine 33cc but I have not had any problems with it last year was the first season with it, handled 8" of ice no problem.
A good sled will help you out a lot too, most guys use a small kids sled you can get at the local hardware store they work well, but do not carry a lot, if you get into it more, I would suggest looking into a nice high wall sled like an Otter for example. The Otter sport sled is a good option and pretty cheap as well. When I first started I found a good deal on a one man turtle shanty, these are nice because they are relatively in expensive and have the sled and shanty together, makes it nice for pulling your whole operation at once.
Shanty: So my first was a one man similiar to the Eskimo Quickflip 1, Shappell FX 100 or the Clam Pro TC 1 person. These are really nice if you know you're going to fish alone for the majority of your trips. Since I started, I have been lucky enough to find a girlfriend who wants to get on the ice, so I upgraded to a 4 man popup, this is another knock off brand, Killzone which ended up being 80 bucks shipped about 3 years ago. The rule of thumb for me and shanty's is subtract a person from the advertised size, i.e. my 4 man could fit 3 people comfortably but is really nice for 2. Generally, unless you've taken a shower recently and really like your buddies, a shanty is going to be smaller than you think.
Heater: This is clutch, I started with a cheap mr. heater exposed coils heater with 1/2 lb propane (Mr. Heater MH15) , works really well, but it's loud as heck and takes up some space, plus it's not the safest thing in the world either and sucks down propane like nobody's business. I since have upgraded to a big buddy with pilot light and fan, the thing is great and can run 2, 1/2 lb propane or from a 20lb. When you get one with a pilot light remember it will more than likely go out unless you're in a shanty, the wind will take it out pretty easy. That's where the MH15 will beat the buddy heat systems.
Gear: I run spinning rods, actually build them myself, I know a lot of guys that will hand line or spool line, so it's really a personal preference, try as many different techniques out as you can, learning from the other folks on the ice. I wish I could give you more advice on this, but in my experience, the minute someone says something about terminal gear a fight breaks out.
Clothing: Just wear a lot... I can tell you what I wear if it will help, I usually have a IceArmor poly blend hat, Frabill fingered -50 gloves, cabelas brand ice fishing bibs 700 thinsulate with knee pads, lacrosse alpha ice king boots (single best ice boots i've ever had).
Tipups: If you're going for pike this is critical, I run some artic fox tipups when it's around 30-40 degrees out and I recently switched to the Frabill 1660 pro thermal tipup for really cold days, it helps insulate the hole and prevent freeze up. I run just the standard 20 lb tipup line with a leader specific to the fish, pike and tigers - nylon coated wire, trout - mono tied with a double uni knot to the 20 lb line.
Any other questions feel free to post or message i'll try my best to answer if I can. Let me know if you want to go out, I'll be going as much as possible, I'm down in Moscow.