Here’s my recommendations for a good starting setup. I’m not affiliated with any of these companies, I just like the gear. I’m sure others will have differing opinions and you are certainly free to do as you please.
Clothing: Well insulated overalls (water/wind proof recommended), well insulated water/wind proof coat, fleece tops and bottoms, wool socks, polypropolene underwear, water proof boots rated to at least -40, Goretex/Thinsulate gloves, fingerless gloves, stocking cap, sunglasses. You might consider cleats for your boots.
Auger: 6" Strikemaster lazer ($80-90) for typical fish under 20"
Accessories: Metal ice scoop, safety picks that go around your neck, 5 gal bucket, camp chair, ice sled.
Rod/Reel: Berkley lightning ice rods UL to ML ($15 each), Mitchel Avocet reel UL ($20), Eagle Claw in-line reel ($25 - 30). Just don’t get South Bend or HT reels. You want good metal spools, not plastic, with good drag!
Line: 4 to 6 lb. mono Trilene ice or Northland Bionic
Lures: Custom Jigs N Spins, Lindy and Northland Tackle all have great stuff. I recommend getting some small spoons, 1/16 to 1/8 oz, like Northland Rattlin Buckshot or the Lindy Rattlin Flyer in greens, perch, pinks. Custom Jigs “Demons,” “Rockers” and “2-eye” in green, pink, black, chartreuse. Custom Jigs “Ratso,” “Shrimpo” and “Rat Finke” in similar colors. Maniac Custom Lures offers some good plastics like Cuttr bugs. Get some tube jigs 1.5" to 2.5" in white, browns, pinks. Lots of competing companies with similar alternatives.
Bait: Night crawlers, wax worms, maggots (eurolarvae), Berkley Gulp products, salmon eggs, Powerbait.
You can find lots of this stuff on fishusa.com, sportsmanswarehouse.com, websites for Northland Tackle, Lindy and Custom Jigs N Spins.
There is a never ending list of stuff you can purchase but this will get you started well. Feel free to ask any questions about above stuff or whatever. Ice fishing is great if you have good gear.