The other replies have covered the basics, but I’ll give my two cents. I’m one of the sick, twisted few that enjoy ice fishing over just about anything and I don’t even bring booze most of the time.
1) A 8” hand auger would be a good starting point. You can often find them used and even new Mora or Strikemaster lazer augers are relatively affordable. Even better get a cheap adapter and attach it to the cordless drill you probably have at home. BAM you have a power auger.
2) While you certainly can ice fish without electronics, I would consider it a form of torture. You’ll catch more fish and have a lot more fun with one. As already stated you can get a ice transducer and shuttle for what you already have on your boat. Otherwise, a vexilar fl-8 flasher can be had for around $200 used. Sell it if you don’t like ice fishing.
3) I’d generally recommend smaller (500 or 1000) sized spinning reels for ice rods. $30 seems to be a good compromise on affordability but not being a piece of crap. A good ice rod can be had for around the same. Or pick up a rod/reel combo. A 26-32” ML with 4-6 lb mono is a good all around setup for perch, trout, walleye, etc. Tons of other information online if you fish for other species.
4) Some small jigs (tungsten, rat finkees) and 1/16-1/8 oz spoons (Hali, buckshot, etc) can catch all the aforementioned species tipped with maggots or minnow heads.
5) For safety, I would highly recommend a spud bar and hand picks. Maybe even a life jacket if going out on early season, sketchy ice.
6) A sled isn’t a bad idea for carrying everything out. Five gallon pail wouldn’t hurt either for keeping fish, storing stuff and as a traditional ice fishing seat.
That was long-winded but hope it helps!