I believe you are speaking of the order of precedence for a combined or massed parade e.g. Brigade Parade. This is set out in the CF manual. Basically for the purpose of parading it is Armoured, Artillery, Engineers, Sigs, Inf, Log, Med, and Military Police – the units that you would see in a Bde. Other factors on a Bde parade would be RCHA takes precedence over Armoured, but air defence is an RCA unit so, after Armoured. If two Inf Regt in the same Bde, the senior Regt first. The Svc Bn has both Log and EME so they parade together, with EME leading as it has precedence before Log. If for some odd reason the Gentleman Cadets of RMC where present, they have precedence, right of line before all Bde units.
Right of the line in the 18/19th century was sometimes awarded for outstanding combat prowess. A place of honour when the formation next paraded.
Also there were soldiers who were called the Forlorn Hope. They volunteered to be first into the breach to get it cleared for the main attack. They were promised a bounty if successful (and lived). Sometimes wore a white arm band for identification. Special Forces of the day, with no special training. Usually tough, brutal men, who gave no quarter. Some desperate for plunder for personal reasons. Some drunks.
When I joined the Army, we had the Stickman. The best turned out soldier on the AM Pl parade, was named the stickman, and became the right marker for the day. There was stiff competion for this honour. This eventually evolved to course senior, and stickman phrase was dropped (too bad). IMO, we should go back to Stickman as a form of incentive, especially on BMQ, etc, but not daily, AM, Pl inspections for trained soldiers.
I am sure there are tons of Army history buffs out there to correct me if I am wrong.