Fire --
The Army changed unit designations promiscuously throughout history. The oldest active regiment is the 3d Infantry. Unlike Brit practice the numbers do not indicate precedence or "rank" among the regiments. Oldest unit in the Army is a company (maybe battery) in MAARNG which has lineage to the early 1600s. Only a handful of regular units have any participation credit for the Revolution; many east coast ARNG units have these streamers.
Regular regiments were numbered from the beginning, but units were disbanded or numbers just changed for the heck of it. My old unit, the 35th Infantry can only trace it's lineage back to circa 1916 and at that time was one of the highest numbered regular regiments.
Before the creation of permanent divisions in WW1 all National Guard regiments had state numbers, such as 7th Ohio Infantry. When these units were federalized during WW1 they were formed into divisions and given federal regimental numbers. Few, if any ARNG regiments were at war strength when federalized, so several were often combined into a federal-numbered regiment. I explained above how the regimental numbers were determined.
I've a list at home with the regimental-number blocks but here's my recollection: Regular regiments were numbered 1 to 100; ARNG regiments started at 101; and I think National Army (later USAR) regiments started at 301. Regular divisions ran to 25, ARNG to 74, and NA higher. Note 82d and 101st were National Army divisions (draftees) in WW1 and reverted to reserve status after the war.
After WW1, when the ARNG was reformed the numbering system was maintained even for new units. By WW2 it started getting jumbled again, and is only vaguely in place to day.
I mentioned streamers earlier. Color bearing units (battalions or separate companies) are authorized campaign or battle streamers on their regimental colors. The Civil War streamers can be either Blue over Grey, or Grey over Blue depending on USA or CSA service. CSA service is considered to be US Army service and CSA earned battle honors accrue to current units. These are all ARNG units in the states of the late Confederacy (to my knowledge).
-- Chuck
[Edited for typos]