Can you provide even a rough budget? Like do you have $500 to spend on the 3 siblings? $200? $800?

Do you have any used gear shops near you? Have you tried to troll CraigsList or OfferUp? Even the thrift stores in my town have a camping section - maybe you could get lucky. What about renting options near you (to see if they even like camping)?

What gear specifically do you need? Do you already have 1 tent for yourself (1 or 2 person size)? Do you want everyone to fit into a single tent, or maybe 1 2-person tent and 1 3-person tent?

Sleeping bags can be cheap - if you don't care about the size or warmth. Do you have a specific low temperature you'd like everyone to be comfortable in? Never camping below 40F temps? 50F?

Foam sleeping pads can be cheap. The knock-off brands are even cheaper. I was happy on a foam pad when I was their age, now I prefer an inflatable pad. Do you have a preference?

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Here are some basic ideas:

Sleeping Pad, 2-pack for $56: https://www.amazon.com/Backpacking-Sleeping-Portable-Waterproof-Moistureproof/dp/B097T75411

Sleeping Bag, 40F rated for $90 each: https://www.amazon.com/Kelty-Synthetic-Backpacking-Sleeping-Regular/dp/B082P5VGGT

Backpack, 60L for $90 each: https://www.amazon.com/TETON-Sports-Ultralight-Internal-Backpack/dp/B01JYY7LEK

Tent, 2-person for $110: https://www.amazon.com/Naturehike-Cloud-Up-Lightweight-Backpacking-Footprint/dp/B07HSZXCC2

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3 sleeping bags + 3 sleeping pads + 3 backpacks + 1 tent = $741 + tax.

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The sleeping bags aren't the lightest/warmest/smallest - but they are fine for starting out. May be long for the 14 year old, but they will grow into it.

The sleeping pads are very basic - but they keep out the cold and provide some comfort from the hard ground. They are bulky - so definitely need to be strapped to the outside of the pack.

The backpacks I typically would never recommend - but they will do the job. They may not last long or be super comfortable. Under $100 each is very low budget. Typically good backpacks cost $200 each.

The tent is a knockoff of a popular model. Not built with the best materials - but it's light and packs small. Tight for 2 adults, but 2 of the youngsters should fit in there well.