Buy a good hand auger (strikemaster lazer for example) for 79.99 or a cheap hand auger for $39.99. Don't buy a used one unless you replace the blades or have them sharpened.
Even if you have to drill through 12-20 inches of solid ice, it isn't that bad to pop a couple holes with a hand auger.
Shelter--don't need one--wear many layers, hat, gloves, etc. and just fish outside. Also, check the weather, don't go when it's going to be a blizzard.
Then get some kind of a chair or bucket to sit on, and sit back to the wind
Wool socks and good boots are the key really.
If you really need a shelter, just buy a used one. You can find one used for less than $100. My first season, I spent $100 on a hand auger and shelter. Still have both--they sit in the garage next to my $450 auger and $250 shelter
If you must insist on renting, I will rent my old shelter and hand auger to you for $300 for the season