Not sure if the endurance bike in question is for you, but let's assume it is since you indicate a "yet to buy" in your profile.
As mentioned, no need to spend huge amounts of money on your first long-distance ride. Some of us here have started with inexpensive (incl. used) bikes to test the waters. In the process, you might even realize that you enjoy biking a certain distance, but the enjoyment might quickly diminish after that. The long-distance thing is not for everyone. The most important thing that you'll hear over and over again is "fitting." It's not easy to get this right. Even among fitting professionals there are disagreements on methodology. It takes a lot of trial and error. It's very likely that you'll go through several saddles, stems, handlebars, pedals to find the "sweet spot." I think for me a good rule of thumb is that if you can do at least a full century ride with little to no discomfort, you've got a good fit. The adjustments that you'll make for the longer distances will most likely be minor.
You could start, for example, with a used steel frameset from the 80's (e.g., Raleigh, Miyata, Bianchi, De Rosa.) Then build it from scratch with the help of someone who is knowledgeable about long-distance riding. Then ride that bike for at least a year doing several century rides and brevets. I suggest not spending on top-of-the line new components on the first bike. Go with mid-range components or buy some great used ones in good condition. It's best to save the money until you know what you want out of a bike. At that point, you might even go with a full custom ride - the best you can afford, if that's still what you want.
If you'd prefer going brand new, there are so many bikes out there in the endurance category. Unfortunately, I don't think there is any bike shop that will let you ride a full century ride and then return the bike if you didn't like it. For starters, look at Volagi, Cannondale, Bianchi, Cervelo, Specialized, Trek, Giant. Just about every manufacturer has one. Try to anticipate a bit your own needs. Some people want fenders (many new bikes don't have eyelets or space in the frame for fenders.) Some people want a rack and bag of some sort (again eyelets needed on the frame) while others prefer frame bags or even backpacks in order to save weight. You'll need to have lights for the longer events whether you want it on the bike, helmet or both. Some riders prefer skinny tires while others prefer wider, cushier tires (some frames don't allow tires over 25-28mm.) As you can see, lots of personal preference goes into the mix.
There is really no point in describing what makes a good endurance bike, except for what I said earlier: if the bike is still comfortable to you after a series of long-distance events, you've got yourself a good endurance bike. Upgrading to a new frame with lightest top-of-the-line components, etc. will represent changes in feel/comfort that might be appreciated with diminishing returns, but could make a difference between a 200 Km. brevet and 1,200 Km. one. This might be where the $10,000 bike could make an impact over the $2,000 bike. Other than that, the $10,000 bike might be akin to giving a bottle of Petrus to someone at his first wine tasting -- it will go in completely unappreciated.