There are three or four small arms called the M-1, and a tank. What specifically does the number after the M refer to in the US military, and how is it selected? The M-16... was it the 16th something?
How do they decide when to recycle a designator? What does it mean?

Model.

I would have to try to find a source to answer your question, but I don't have my own computer with bookmarks with me here. Theres obviously a rough chronology that goes along with the model numbers, once they stopped using years of weapon introduction.

Unfortunately, it is inconsistent.  For example, there was the F-4 corsair of WWII as well as the F-4 vietnam era jet.  2 Entirely different aircraft with the same designation.  Usually, M for Model, then the number.  The M-2 would be the second of the series (Not sub designation as in M1A1)  Then, some times it is based on the year of release.  The M 1911 and the M1921 are examples.  It is basically whatever wild hair crawls up some Genitals anus.  

I've noted the inconsistency... actually, I'll settle for "what does the US use these days".

http://en.wikipedia.org/wiki/Army-Navy_Equipment_Code_Designators
Thats only for electronics. I am trying to find weapons for you.

Quoted: Even test models are given a model, but they may not be adopted.

Those are usually an "XM" designation.

M means it was developed by the US Army
Mk (mark) means dept of Navy
L for British, for Land services
DM for Germany

Most NATO counties follow this naming convention.  

The numbers are assigned in order to items of specific type.  So a pistol gets it's own number series, and a rifle it's own, and a carbine it's own, and a wheeled vehicle it's own, and a tracked vehicle it's own.  So you can have many different items with the same number, they just won't be the same type item.

An example of this would be in WWII.  The M1 Rifle, The M1 Thompson SMG, The M1 carbine, the M1 "steel pot", the M1 ammo can (.30cal), and so on.  We bought so much new stuff at once for WWII, that there was alot of "M1" during that period.

Before WWII we used year of adoption.  That's why you have M1911A1 pistol, or M1903A1 rifle.  It gets confusing though when you buy more than one thing.  for example the M1917 revolvers were two entirely different guns, and today would have different numbers, but because we used year of adoption they were designated the same.

So when the powers that be saw the war coming, and what it would require, they changed to the "M" system of the time.

Today's system is a more refined and evolved version of that one, though there's alot of inconistency between the two due to changes and time.

"M" means model
"X" is a prefix used to designate an experimental model
"E" is a suffix used to designate an experimental variant
"A" is a suffix used to designate an adopted variant.

So an XM4 Carbine is the experimental model of the 4th carbine.  When it's adopten the "X" is dropped and it becomes the "M4 carbine".  It's the 4th carbine because the Army simply hasn't messed with a carbine sine the M3.  So the next one is M4.

The M16A1E1 was the first experimental variation of the first adopted variation of rifle 16.  There's a big void between M1 and M14 that can't really be explained, other than saying the system changed during that time and that's just how it ended up.  From M14 on though, the system is constant.  There was an M15 and then an M16.  Anyway, once adopted, the M16A1E1 became the M16A2.  The second adopted variation of the model.

During experiments and trials, if there's a possibility that the weapon will be adopted, then it's assigned a number.  So not everything that gets tested gets a number.  Just stuff that might go the distance.  So when the Army tests several things, like for the SAW, you get the XM249, and the XM248(Ford Areospace), XM262 (HK), XM106 (souped up M16) contending.  When the M249 got adopted, the others drop by the wayside and those numbers aren't used.  That's why you get gaps in the system from one number to the next serving number.  In between the two numbers in use, there was an experimental that didn't make it.  This allows the Army to go back and resurrect something if it turns out it's needed wihtout alot of confusion.

There are inconsistancies of course, as this is the Army we're talking about.  The M9 pistol was numbered "M9" regardless of the model.  They were all "XM9".  So you get weird stuff alot.

Tracked vehicles run on the same number series.  So you have an M1 tank, an M2 Brad, an M3 Brad, an M4 Brad, and on.  The M8 AGS was the XM8 in testing.  And so on.

Wheeled vehicles have their own.  Which is why you have M1008 and so on.

The assignment of the number is done by the proponent agency within the Army that's responsible for that piece of equipment.  Even if a number is assigned incorrectly, the Army will keep that number and use it unless it's going to cause alot of confusion.  The reason being is that it actually costs millions to change the number of a weapons program once it's going.  Changing everything over to a different number costs alot of money, and is why the "X" is used.  Parts, publications, and all logistics support remains the same and even old stuff with "XM" on it can be used safely with minimal confusion.  If you had an M4 carbine with an "XM4 Carbine" manual, it wouldn't be so confusing that you couldn't use them.  If you had an M4 Carbine, but a maual with "T556" on it, it could be very confusing at the troop level.

Navy stuff is bought with the "MK" designation in place of "M".  "Mod" is roughly the same as "A".  A MK19Mod3 40mm was originally developed by the Navy for river boats in Vietnam, and that's why it's still the "MK19" today, even when used by the Army.  The proponent service names it, and eveyone else uses the same name to prevent confusion.  The Navy handled the MK23 pistol, even though if used in the Army it will still be "MK23".

We had a thread on this a while back, with the appropriate nomenclature defintitions quoted from the manual. Can anyone do a search for it?

(It referred to the nomenclature of the M-4 Carbine)

NTM

The old Navy plane naming convention was somewhat consistent

Type-Sequential Model-Manufacturer

F2F, F3F, F4F (akaWildcat), Fighter-2nd model, 3rd model-Grumman

F4U- Fighter - 4th model-Vought

R4D Cargo 4th Douglas

A1D Attack 1st Douglas

TBMs, TBFs TBDs  basically the same plane but built by General Motors, Grumman, Douglas.

Quoted: Unfortunately, it is inconsistent.  For example, there was the F-4 corsair of WWII as well as the F-4 vietnam era jet.  2 Entirely different aircraft with the same designation.

They don't have the same designation at all. The Corsair is the F4U, it has never held a modern designation like F-4, which I believe McNamara or someone developed. They are two different naming conventions. PaDanby describes it in a previous post.