Mobile Suit Model Numbers in the Early UC Timeline

There is some sort of pattern to it

If it is a Federation MS like Gundam (RX-78-2) or a GM (RGM-79) or the Marasai (RMS-108) it typically starts with "R".
Within the Federation MS model numbers there are other codes as well:
-The "GM" in RGM-79 is for General Mass Production
-The "X" in RX-78-2 usually implies a prototype unit
-The "MS" in RMS-106 Hizack or implies a Zeon based unit or in other words a Monoeye.
-The "B" is for Ball as in RB-79 Ball and its variants.
-The Jupitris has its own code "PMX" as in the PMX-003 The O, the "X" is again for prototype units
-"_RX" (any letter followed by RX), is usually a prototype transformable unit like the ORX-005 Gaplant or MRX-009 Psyco Gundam.
-"RGZ" is for Zeta Transformable type like RGZ-95 ReZel and RGZ-91 Re-GZ.


Zeon usually had simply "MS" for Mobile Suit (MS-09 Dom).
There are plenty of variations of this:
-Amphibious units add an "M" to the end for an "MSM" designator like MSM-07 Z'Gok, likely "M" is for Mariner.
-Trial machines are labelled with a "Y" at the beginning as in YMS-15 Gyan or YMS-14 Gelgoog (later MS-14A after passing trials).
-Newtype-use add an "N" to the end as in MSN-02 Zeong
-The Mobile Armours are typically labelled "MA", like MA-05 Bigro, adding an "X" is for prototypes like MAX-03 Adzam, or adding an "N" is for Newtype-use like MAN-08 Elmeth


AEUG follows the same trend as Zeon but always adds a third letter "MS_"
-"K" is for Karaba MSK-008 Dijeh
-"Z" is for Zeta transformable type, as in MSZ-006 Zeta or MSZ-010 ZZ
-"A" is for AEUG as in MSA-003 Nemo and MSA-005 Methuss


Axis
-"AMX" for general purpose Mobile suits like AMX-011 Zaku III or AMX-009 Dreissen
-"AMA" for Mobile Armours like AMA-01X Jamru Fin


Neo Zeon
-"AMS" for general purpose Mobile suits like AMS-129 Geara Zulu
-"NZ" for custom Neo-Zeon units like NZ-000 Quenn Mansa, and  NZ-333 Alpha Azieru
-"MSN" is reused frequently same line as started with Zeon, MSN-04 Sazabi


That is pretty much it in summary, there are of course many exceptions and a few that just don't fit the pattern. I only covered early UC, because for the most part the AU series and late UC are actually much more consistent and thus far easier to follow.