Simply put, all BHPs marked "Browning Arms Company" (BAC) or "Fabrique Nationale" (aka FN, FNH, FNH-USA) are the same creatures - made in the same factory by the same people.
That said, the basic model currently is the Mark III. Whether it has fixed or adjustable sights, different finishes - what ever, the pistol started life as an unfinished Mark III.
I just say here that the topic of clones (Inglis, FEG, etc.) is a very lengthy subject for later discussion.
That said, we then progress to earlier models. BAC didn't actually begin importing and selling BHPs in North America until the early 1950s (marketing license agreements between JMB, Colt Arms and FN).
Of the early pistols, the "T" series (produced from 1964 through 1969) are considered the pick of the litter. Almost mystically, they seem to have better triggers and fit and function.
The "T's" were followed by the "C" series. Subsequently, there was the Mark II which has a small rib on the top of the slide and somewhat better sights than the earlier models, parkerized finish and a factory ambi safety (on late model pistols).
The Mark III brought better, larger, dove-tailed sights, ambi safety, a firing pin block (on the sear lever), a durable enamel matte finish and a larger ejection port. Originally, they, as were previous models were forged, but current frames and slides are cast - and reportedly stronger.
Minor points:
Early models had strong side only safeties - small and hard to operate under stress, but easily replaced with C&S extended safeties.
Sights on the earliest models were typical mid-20th century type (think military issue 1911 and you have it).
Pistols produced before 1960 had internal extractors (again, think military issue 1911 and you have it). All later models have external extractors.
What to buy? That depends upon whether you want a "shooter" that you can shoot, carry, keep you and kin safe or generally have fun with --- or a "museum piece" that is looked at, cared for and treasured for its originality and historical significance but rarely shot. That is a decision only you can make, and rightly so. After all, it is YOUR money and it will be YOUR gun.
My self? Every pistol or rifle I own is meant to be used. While some were purchased for their history, they are all "shooters". They go to the range, get used, cleaned, repeat, repeat, repeat - and to me, that is as it should be. So for me, any used BHP would do if I was in the market for another BHP. If I was buying one for a family member just starting out, a lightly used or new Mark III with fixed sights would be my first pick.
I hope that helps.
