What you plan is a big step but "Do-Able" with the right attitude and precautions. You have ask most of the correct questions, to begin with. You are also starting from a good position, I am also retired US Navy, however I began sailing/cruising early in my military service, about 1960. I also learned boat building, both wood and fiberglass, from an old sailer/boat builder mentor. I started out acquiring a series of older wooden boats for local coastal cruising in So. Calif. Once I was stationed where I could build a boat I set did just that and several more followed over the years. In '90s, just before my second retirement, I began building an Ingrid 38 from "bare hull'. This boat took me 9 years to build and another year to fit it out.
Now, I'm not suggesting everyone should go this route. There are plenty of affordable cruising boats that can be outfitted for world cruising. And there are even more that shouldn't go beyond the horizon. It is true that some of the latter have done extensive open ocean cruising but at some risk..
There are as many opinions on this subject as there are boats for sale (don't be swayed by the broker or the guy who wants you to buy his boat). Take you time and study this topic and visit/correspond with happy cruisers. Read cruising books.
You notice I keep referring to "Cruising.. that is because the majority of the ocean cruisers are just cruising and very few are "Circumnavigating..". This is not to say a cruiser can ultimately circumnavigate. It all depends on finances, family commitments, health and the boat you set out on. You notice I don't mention age since I have never allowed that to limit my dreams. (I'm 72 now and feel that I could still do it.)
Regarding your questions about titles/liens titles and inspection. There are two ways that boats are titled in the US. State registration, where there are numbers on the bow area of the hull and then there is a USCG vessel documentation. If you purchase a state titled boat, you can as to see the title. It should show any lien holders in addition to the owners name (states very). A USCG doc. vessel is better since you can get an Abstract of Title with the Doc. Number and $25. Only takes about a week and is worth the fee. It shows the entire ownership history, preferred mortgage holders, tax liens, etc.. In most states, you don't have to bother with state registration if the vessel is documented nor do you have to display any numbers on the hull. The USCG Doc. number is engraved into the hull and remains with the vessel as long as it remains under US citizen ownership. A documented vessel is considered a "Preferred Mortgage" by most lenders. Also I you don't pay any annual fees, just return the renewal card each year and they send you a new Document. You still have to pay state sale and property taxes and this is where some owners get into trouble since the state or local tax authority will just place a lien on the boat and eventually they will have to be paid before he can sell it.
You will want to have a marine survey for any boat you finally find that you think you want to purchase. This is usually in the final purchase process and will be combine with a 'haul out' so he can inspect the bottom. I warn against excepting the sellers or brokers recommendation on surveyors. They will most likely be predjudiced towards the seller. Ask around other cruisers/boat owners. If the seller offers a previous survey "to save you the cost" except a copy for your information but opt for your own. The cost of a survey is not cheap and varies with area. In So Calif. for a full, out of water, it will be around $20/ft. plus the yard fee for an inspection in the slings, usually about an hour. It there are any major problems that the seller failed to disclose, you can require that he stand these costs. Talk to the broker about this contingency.
Where to shop or how to shop.. One of the best ways is to try crewing on various boat types, preferably off shore or at least out into open water. Or once you find a type you think is close to what you want, find the same boat in a charter fleet and take one for a week of so.. You sailing certificate would help you do this.
Make friends with cruising type boats and offer to crew with them. And keep in touch with this forum and a few others around.
s/v Good Intentions (Ingrid 38)
m/v da Wave (Huckins 53)