As has been mentioned, Combination squares tend to give you a better return on your money, and might be better to start out with.
Starrett is considered the standard by which combination squares are evaluated.
Starrett manufactures their square in both cast iron heads, and forged steel heads.
Forged steel is the high end option, but both will work.
The head material type on the Starretts can be determined by the finish.
Cast iron heads use a crinkle finish.
Forged steel heads use a shiny black enameled finish.
Starrett manufactures the square in a 4”, 6”, 12”, and 24”, sizes.
The “size” is really based on the nominal rule length designed to go with the square.
The rules for the square have markings on both sides, that are reversible.
Metric versions of the rules use different blade lengths to correspond with a standard metric length.
In some cases, such as the “ 12” rules” there are longer blades you can get, such as 24”, although the 24” “jumbo” combination square, is a different model, with a larger head.
The rules are, or were, available in mat chrome, as well as bare steel.
Most people prefer the mat chrome.
There are also “double squares” which function like a combination square, but with have a straight head that reads 90 degrees on both sides.
These are available in the 4” and 6” sizes above, like the Starrett combination squares, and in a 2-1/2” size, for more precise work.
While Starett is the “gold” standard, PEC tools, also in the USA, makes a decent combination square, and likely supplied other major metrology companies, like Mitutoyo and Browne & Sharpe with combination squares.
PEC also manufactures double squares.
Epstein tools had some deals on “seconds” on the PEC squares if you need to save some money.
Most combination squares, at least the quality ones, are usually somewhat interchangeable parts wise for the heads and rules, in similar sizes, so you can buy a square, and update parts later, adding longer rules, or metric rules, etc.
I might recommend a double square as well as a combination square.
Another advantage to combination squares, is that the fit of the rule to the head can be adjusted if it goes out of accuracy.
Something that is way harder on a fixed square.
For fixed machinist squares, I usually prefer the European designs that are made from a single block of steel.
A small high precision “00” grade one can be used to check combination squares for accuracy.