I was interested in buying a private mine, but didn't find really any information on the Wiki except for where to buy and how much they cost. So, I got some caps together and purchased one from the Junktown mine overseer. All the information The wiki on private mines is here ->
http://fo2238.fodev.net/wiki/Mines#Private_MinesSo, for 75k here is what I got:
Outside
Inside
Even though I bought it near Junktown, the private mine is located in the Redding area. Inside the shack there is a table with "Stuff" on it, that I can store items in. There is also a waterpipe outside, though I don't know if the waterpipe depletes or not since I haven't used it yet.
Of course, knowing that the resources would deplete I mined the thing until it was completely depleted, and saved all my gathered materials. The final count was 148 minerals, and 109 iron ore. This is NOT a HQ mine, just standard ore and minerals.
Other things to note are that it is indeed private. I had two friends tagged on me, and right next to the mine overseer when I bought the thing. They also traveled to the mine for the first time with me, and they do not have access to it unless I take them there. There is no way to give them access.
So, basically I have a really nice private area that cost me 75,000 caps. For mining, it isn't worth it for the price. Stick to the unlimited public mines. If you want an extra private area to store items or park cars, well, then the value is subjective and you can make that determination yourself.
Whether or not the location or number of resources available is typical, I don't know. This is just my experience, and I thought I would post it since there isn't much info on the Wiki about it.