Great Grandmother's Collection

I've recently been gifted a beautiful stamp collection. There are some very old stamps, and I'm wondering how to find their value. I'm not planning to sell anything, but I want to make sure the relative who gifted this to us is aware. They belonged to his great grandmother, and he's very young, and he gave them to us because he thought we'd like them (they are American stamps and we are his American relatives). This is the stamp I think is the most rare in her collection, based on my preliminary research.

Scans are greatly preferred to cell phone camera pictures, whose poor resolution makes hard-to-see details that make the difference between valuable and common impossible to discern..

There are people on this site who can and will help you. What is needed most are good scans of the stamp. Sometimes the front will do and sometimes front and back scans are needed to evaluate what you have. What you are showing is probably a Scott Catalogue #65, but could be a different Scott number as there are several associated with the image you have shown.

The stamp that you pictured is from the 1860s so it is old, but not necessarily rare or valuable. As others have said, a better picture would help, for example the black marks at the bottom could be a postmark or cancellation, making this stamp worth around a dollar on a good day.

If the marks are just scuff marks or lint on the photo and the stamp is unused with full original gum on the back, then the "catalog value" for an unused #65 is $125, but the retail value in that condition (toned perforation at the left and is that a small tear at the top above the U?) makes it worth maybe $15-20, but could be a lot more or a lot less depending on details that a sharper photo may be able to discern.

What leads you to believe that this is the most rare stamp in her collection? There are many subtle varieties of that stamp design (mostly different color shades), some worth hundreds or sometimes thousands of dollars and this is unlikely to be one of those, but can't really say for sure from this photo.

What are some of the other nice stamps in the collection that were adjacent to this one? Sometimes "guilt by association" can help determine whether this stamp is worth more research if the collection had a lot of other scarce stamps. Or if everything else in the collection is fairly ordinary then 99.9% chance that this is also one of the common varieties. It can still be a valuable sentimental memento from a relative and artifact from a time long ago, but not of much collectible or economic value today.

Old does not often equal rare.
Rare does not always mean expensive.
Stamps hide their important points from all newcomers, it is part of the draw to this philatelic pastime.

Now here is a question back at you: Does your stamp have a grill? Say what you say? What the heck is a grill and how does grilling help me with stamps? Do I see better when I am not hungry?

Seek out a stamp club near you. Members there can help you evaluate the collection, or refer you to someone who can. Go to the American Philatelic Society (APS) website at https://stamps.org and select FIND A STAMP CLUB.