For serious modelers, there are many choices of military models to build.  The kit manufacturers consistently add new items and the quality of the kit materials have greatly improved over the years. Essentially one can build in three categories: Armour, Aircraft or Warships.  Within these, you can typically select from the U.S., German, Russian, and Japanese militaries, and from WW I, WW II, or more modern eras.

Armour:
This is a very popular category because there is an almost endless selection of vehicles and most are 1:35 scale, which makes for an ideal size: big enough for lots of detail but small enough not to take up too much space for display. Armour in 1:35 also allows for the creativity of Dioramas (scenery using your model to tell a story) and the use of figures, which can make each build unique.

Aircraft:
Building model airplanes as kids is where most of us started. The more experienced modelers today have a large variety of aircraft to choose from, and with more choices of scales than armour. Many choose 1:72 which offers more display space and good detail. The 1:48 scale is probably the most popular now, and there are some good kits using 1:35. I prefer 1:48 because most kits (and their aftermarket accessories) are in that scale and it seems the ideal size to show extremely good detail. As in armour, many choose to display their aircraft models in a diorama.

Warships:
Building model warships is a significantly different category than armour or aircraft. Over the years, I have built all categories, although in the past most of my builds have been warships. There are many ships to choose from, though most have a well-known and historical reason for the kit manufacturers to produce them (such as the Arizona or Bismark).  

Some kits arin 1:700 scale which helps with display space, but most are in 1:350 scale and have always been my choice as it provides for building good detail (if you are patient), while still finding room on a shelf or display case. Recently, a few models have been offered in 1:200 scale which can provide for a long-term project with amazing detail as long as you have room to exhibit your skill. (The 1:200 WW II aircraft carrier Enterprise by Trumpeter is 49 inches long).

Many modelers never build them, for several reasons. Besides taking up too much room, they take much longer to build, involve difficult rigging, and use a lot of PE (photoetch) to add ladders, railings, radar screens, small boats etc. For many, bending the tiny brass PE pieces and installing them all over the model requires just too much time and patience. I see this often myself, but when finished, there is something very special about a fully fitted out battleship in 1:350 scale on display.