First off, I would suggest that you do determine exactly what the mineral interest is that you do own. As you indicated, this just involves a records search and someone reputable, be it an attorney, professional landman or title company, can usually do this for you without too great an expense, especially given the sum of money you have been offered. Remember that almost all mineral deeds and leases contain a clause stating that you warrant and agree to defend title to what you you have leased or sold them.
It is very common these days for the lease or deed to read that you are leasing/selling "all (or a fraction, such as "one-half") of your right, title and interest in and to . . ." certain tracts. I like this language better than that specifying a decimal interest (i,e., "a .03756 interest in and to . . .") ownership.
As I'm sure you are aware by now, a lot of the responses are from mineral buyers, brokers or landmen. If you are seriously wanting to sell, this can be a good thing, as you'll usually wind up with a multiple offers.
I would recommend that you be very careful, though, as there are bad apples as well as very good ones in this business. Some really know their business and can be very helpful to you at all stages of a potential transaction. Others know little about what they are doing, have no professional credentials and just see an opportunity to make an easy, quick buck. The problem is how does someone like yourself on the East Coast with little real knowledge of the petroleum industry separate the wheat from the chaff, so to speak.
The Texas Counties of Culberson, Reeves, Loving, western Ward and far western Winkler, plus parts of southern Lea and Eddy Counties in New Mexico, make up the Permian's extremely prolific Southern Delaware Basin play. It is without question one of the hottest onshore unconventional resource plays in the world right now. So there has definitely formed a "boom" mentality in that region, and everyone wants a piece of the pie.
Be sure to ask for detailed information about the individual/company you are dealing with in each case, get verifiable legitimate references and require verifiable information as to who the actual end buyer is. Find out how long the the parties involved gave been in business and if they do have professional credentials, check them out. Remember that someone who is brokering acreage or speculating that they can promptly turn your minerals for a profit will more often be offering you a lower price per net mineral acre than someone who is, or represents exclusively, an end buyer.
I would strongly recommend that you ("Grantor") do not sign a mineral deed to any party ("Grantee") without getting paid at the time of signing, preferably with a cashier's check. An instrument that used to be sent in the mail with a lease or deed in the past that protected everyone is called a "sight draft", but I haven't been paid using one of those in years. If someone offers you a deal you decide to accept, and they want you to sign a deed and then give them days, weeks or more before they have to pay you, I strongly suggest you don't do it. Remember that a buyer will often need time to do "due dilligence" after you come to a verbal agreement. However, a less than scrupulous party may really not have funding to buy your minerals and need the executed deed from you to try to find it. And they may never get it, keeping your minerals tied up for a long, long time.
I hope you find some of this information helpful. I know it does not address the question of "what is it worth?". Geological and engineering studies or reserves estimates are usually expensive and complex. Further, they are only as good as the assumptions that underlying the numbers. Numbers can "prove" anything, given the right assumptions. This is not to say that such studies cannot be valuable, but the cost on for an interest no larger than what you described would probably be prohibitive. The best I could recommend would be to watch websites like this and compare what you are being offered with what other mineral owners say they have been paid or offered. You don't want to give your minerals away, but holding out for more than anyone else is getting might not be the wisest move, either, if you think you do want to sell. And remember, just because someone got a certain amount for their minerals in a section a mile or two over from you, it doesn't that yours is worth the same. It could be less, or it could be more. Many buyers are very "tract specific" as to how much they offer.
What is important is that you get what the minerals are worth to you, based on what you value. You indicated that the money might help you retire earlier than you could otherwise. You also indicated that you might like to retain something to pass on to your descendants or heirs. Selling part and keeping part might go a long way towards achieving both goals. I almost never sell all my mineral interest in a given property, if I sell any at all.