I especially mean the time period between the 1st century BC and the 2nd AD.
For example, in a campaign in the middle east, where cavalry seems to be more important, would we see legionnairs using spears instead of gladii?
Or, would their armour change to something lighter than mail while deployed in the hot north africa or would they deal with the heat in another way?
So i guess i could ask, besides ligher or warmer clothes would the equipment of a legionnaire vary significantly based on where he's stationed across the empire?
Legionaries did not vary their equipment greatly during the first two centuries AD as they were always armed with pila and a gladius and always armoured, most commonly with mail. From the third century AD onwards you have more variety in equipment of legionaries, this is in part due to the blurring of lines between auxilia and legionaries after Caracalla’s granting of Roman citizenship to all inhabitants of the empire.
By the 1st century BC the triarii, who historically had been armed with spears instead of pila, had more or less disappeared and all legionaries were equipped the same, regardless of their opponent. Rather than change the equipment used by legionaries from engagement to engagement the Romans relied on the specialisation of the auxilia to combat certain threats across the empire.
For example, a lack of cavalry was managed in the manipular armies of the 2nd century BC by using Latin allies. Polybius 6.26 mentions how ‘the whole number of the infantry of the allies generally equals that of the legions, but the cavalry is treble that of the citizens.’
This proved effective against Rome's enemies until they came across the Parthians and their new style of fighting (compared to what they had faced before). The disaster at Carrhae and Mark Antony's Parthian campaign revealed the effectiveness of mounted archers against both Roman legionaries and their allied cavalry units. As a result Rome recruited from Eastern peoples in their empire who were used to mounted archery. This allowed legionaries to stay as heavy infantry as there were other irregular units who could fight in these more specialised roles.
The Roman army was generally very flexible and adopted equipment/tactics from other cultures if they proved effective. Bishop and Coulston's book 'Roman Military Equipment from the Punic Wars to the Fall of Rome' has a good section at the end on this very point. It uses the example of the North African light cavalry so show this. They first fought for Hannibal against the Romans, then for the Romans across the whole empire and by the 3rd Century equites Mauri had become a formal unit title describing soldiers fighting in this way.
I hope this answers you question!