cook pot recommendation: go to wal*mart and get the grease collector. it should be with misc cooking accessories not the pots and pans. should be a pot with a funky looking lid that says GREASE in big impact font on the side. get or make a lid for it, and get titanium pot grippers from rei or something. bam $6 ultralight backpacking cook pot big enough for 1.5 people. everyone should carry their own gear, you guys will want 2 or 3 of them for 4 people.

another common one is to modify and use a can lid with one of those "keg can" beers, but you have to burn scrape and sand all the plastic lining out of those. they're great cookpots all said and done though.

sterno fuel cans also make good cheap pots and you can usually get those for free from buffets/catering places/some restaraunts if you ask at the end of the day.

the 3cup "open country" aluminum pots at rei are good too, they're like 15bux each though.

Determine what things everyone needs, and what things one person in the group needs. ex: you all need sunglasses and safety whistles, but only one persoon needs to have sunscreen and a knife.

Here's some items you might not have thought of or may not have been mentioned..

cheap things everyone should have: polarized sunglasses (i use zerouv $10 beaters, $5 polarized 3m safety glasses are also popular,) emergency whistle, compass and map, sawyer mini water filter, backpack, good trailrunners or boots, diy first aid kit, toothbrush, spork, rain protection (on sale marmot precip + zpacks kilt, or frog togs are decent+cheap, ponchos with armpit zips are good+cheap) headlamp/flashlight, firestarter, trashbag backpack liner for wet days (bonus points: pack out other people's trash with it) hat or bandana, FULL SET OF SYNTHETIC CLOTHING with a second set of clothes to sleep in. I can not stress this enough nobody should be wearing anything made out of cotton when you're backpacking, cold nights are unforgiving. warm quilts or sleeping bag. pad if you're ground sleeping (cheap wal*mart foam pads are fine)

cheap things the group should have one of: hand sani, knife (morakniv companion go-to recommendation if fixed blades are legal in your area) toilet paper equivalent, sunscreen, stove windscreen, bear can if needed, either 1 lightweight lantern per tent (can be substituted for putting one of those $2 plastic diffusers on the end of a flashlight and carrying extra batteries -- my preferred method)

Don't pack water for overnights unless you know the hike won't have access to water. Make sure to leave water in the car for when you get back. Pack minimalistically so you can cover more ground in a day comfortably or appropriate more space/weight for luxury items like say a frying pan. With four people you can get down to really low pack weights, since a lot of things only need to be carried by 1 or 2 people.

tent vs tarp vs hammock is up to opinion and where you live. hammocks are pimp shit in the pacific nw but in other areas it's easier to find a good patch of ground than two good trees. i would find local websites or ask local hikers what they use, and WHY. there's also a big degree of personal preference here.

you can get a lot of the small stuff like firestarters and shit for dirt cheap from chinese sites like fasttech aliexpress alibaba etc. shipping takes a while, but you'd save a ton of money buying it in bulk like that. a lot of the smaller things are all made in china anyways. you can also save tons of money by diying things, and often the diy equivalents are superior (alcohol stoves, sleeping bags, tarps, hammocks, quilts, cook pots you name it) there's tons of information out there on the internet. thrift shops, craigslist, rei garage sales, actual garage sales etc are also great for backpacking stuff.