To my understanding, the standard Pre-Marian battle formation consisted of a layered system in which Hastati engaged first, followed by Principes who would fill in the gaps, and finally Triarii if the shit hit the fan. Cavalry would be kept on the extreme flanks, and a thin line of velites and leves would launch pila before any infantry engagement. That being said, when the Marian reforms occurred, standardization of equipment became a big aspect of that. With that however you lost the layers of experience. So what would the Romans have done as a standard pre-battle formation after that?
Many things did not change.
(Indeed, the "Marian reforms" are generally better understood as a more gradual transformation of the demographic makeup of the legions, combined with evolving tactics as time went on. Marius can be seen as doing away with the pretence that the old recruitment system was still in place and openly admitting capite censi recruits, rather than making drastic changes himself. Though this is debatable and he may indeed have introduced some of the innovations himself.)
The legions of the late republic, the early empire, and even the late empire still formed up in multiple battle-lines. (See Caesar at Pharsalus. See Julian at Strassbourg.) They still maintained unusually large portions of their army in reserve. (See Agricola at Mons Graupius.)
They still fielded light infantry and cavalry to support the legions, though light infantry skirmishers certainly seem to have been fewer in numbers than the Republican Velites. (Which made up more than a quarter of the infantry.) According to Goldsworthy, infantry skirmishing was rarely decisive or very important in ancient battles, so this change probably reflects the greater professionalism and fighting prowess of the full-time legions. The large number of velites would then not have been a tactical necessity but a consequence of the social structure that created the early legions.
The imperial legions did field archers and slingers. The former were often put behind the main battle-line where they would be protected, firing over the heads of the legionaries. (See Josephus on the first Roman-Jewish war, or Arrian's (theoretical) deployment against the Alans.)
The key difference of the post-Marian army was its organisation in cohorts rather than maniples. (Though again, note that the cohort structure had already been in occasional use for a century.) The cohorts were bigger and capable of independent action, and could be deployed or redeployed in a more flexible fashion.
Goldsworthy says, in his "Complete Roman Army," that the legions post-Marius still most commonly deployed in the traditional triplex acies formation, with four cohorts making up the front line and three cohorts each in the second and third. However, the legion could also form in 2 lines, or in 4. Deploying in one single line wasn't commonly done. At Pharsalus Caesar took one cohort from each legion's third third line, and used the thus created fourth line to surprise and defeat Pompey's superior cavalry.
As for layers of experience: certain cohorts may well have been "elite" or veteran than others. Under the principate, the first cohort was larger than the others and is often assumed to be such a veteran formation, though this is by no means certain. Vegetius claims that the first cohort was made up of taller recruits than the others, though we can never be entirely sure if Vegetius is reporting fact or making up idealised fantasy.
By late antiquity, the makeup and organisation of the legions changed a great deal, but as I indicated at the start the battle formations continued to rely on multiple lines, at least in those battles we have sufficient sources on.