Despite the modern myths about it, Teutoburg was a temporary setback — Rome did reconquer the territory lost, and then some. The additional manpower in the form of auxiliaries was used in the Praetorian Guard (which recruited tall men) and throughout the legions on the frontiers. The Romans maintained their German frontier with four legions, total, and their Danubian frontiers with five legions. It’s astounding, really. They had an active bribery policy to reach the tribes just over their borders, and through trade, travel, and native alliances, to keep the tribes peaceful well into the interior where they never went. Of late Roman colonization has been discerned in the Baltic, as well as in Ireland, and that’s probably just scratching the surface.
I don't think Rome ever had any grand scheme for conquering the world. More that they kept going until it cost more than it gained to keep going.
I think Rome initially moved north because Rome had repeatedly been attacked from the north. It was a matter of time before they were overwhelmed if they kept playing defense on that border. It may be that they couldn't afford to stop once they started.
I'm not partisan in terms of who was right or wrong. By our standards, there were no good guys back then.