I have always bought items for my son's gifts at thrift stores, mostly, books. I've received recipe books from thrift stores (they work exactly the same as a brand new recipe book would!)
In my family, we are down to where we pretty much only gift homemade items, if we gift at all. My son usually asks me what I want, so I make an amazon wish list (easy place to put a bunch of different kind of items), and tell him to check out the thrift stores, local restaurant supply store (this Christmas I got a knock box for the espresso machine, something I really wanted, but didn't want to spend the money on for myself, since I was getting by fine without one), etc.
I'm working on making a quilt for my parents (with my sister and sister-in-law), and some of the fabric has come from the thrift store.
I've been putting together a "when you move out" stockpile that I will gift to my son when he goes away to college and/or gets his first apartment. Some of those items were bought second hand and include pyrex measuring glasses, mixing bowls, and cast iron skillet(s).
I've also given vintage lunchboxes I found at a great deal, photo frames, etc.
I keep to things that are unique enough that no one would care they weren't brand new, don't show signs of wear, don't decrease in value (not sure how else to word that-- a glass measuring cup isn't going to suddenly not be unusable, less useful, in five years), etc. Tools can be a good example too. Many older tools were made much better than a lot of the cheap stuff imported now.
For gift baskets, I don't use literal baskets, since no one really uses them. I've used a small (3 gal?) bucket from Home Depot (when they go on sale for $1), a "beach bucket" I found at the thrift store, a tin in the shape of a dog bone for homemade dog treats (found at the thrift store), mason jars for honey (got a gallon of local honey at the farmer's market for $28 one year, so everyone got a smaller jar of honey in their gift basket, and I still had plenty for myself). Tool boxes and bags also work as baskets.
If you do food in a jar gifts (soup, cookies, brownies, etc), you can buy the mason jars at yard sales/thrift stores.
You can make your own gift bag from fabric bought second hand (estate sales, thrift stores, yard sales, etc). We got bags made from a pair of jeans as the wrapping for a gift from my sister-in-law. My mom got half the top, so she was able to loop a ribbon through the belt loop and now uses the bag for a portable knitting project (holds the yarn, needles and pattern, and she can take it when she babysits, has to take my dad to dr. appointments, etc). Mine was made from the leg of the jeans, so it wasn't as easy to add a handle, but I just stitched one on and it's good to go.
For people who want nothing to do with thrift store, second hand items, no matter how pristine condition they come in? I'm not good at deception, so I don't know if I'd just give it to them anyway. I'm more the kind who would not spend any more on them than I do on the others, even if the result is that the value of their item might is less. If I can fill up a bucket for one person using items from the thrift store, and I come to $5 spent, the "only new" person would also get a $5 gift (bought on sale with coupon at least, if possible). If they complained that the person with the bucket got 10x the amount of stuff, well, that's what happens when you value where the item came from over the item itself. Fortunately, I don't have this issue. No one on my list would care if a mason jar or a tin, a book, etc, was bought new or at the thrift store.