Rome had a patron client system in which powerful Patrons would do favors for their poor/less powerful clients, and in return these clients would give their patrons political support. After the reforms of Marius allowed the landless poor to join the army (prior there had been a property qualification) the poor soldiers would essentially become the clients of their general, who would be expected to look out for their interests (as Roman generals were also always politicians). During the late republic this often became a contentious issue. For example Pompey had a running political battle with the senate over settling his veterans on tracts of land, which eventually led him to forming the triumvirate with Caesar and Crassus. From what I understand veterans often expected land after their service in addition to a share of the spoils of a successful campaign. I'm less clear about the earlier republic (service was obligatory for property owners) and the empire though

Under Octavian, there was a system whereby Roman soldiers would be provided with either money or land upon the conclusion of their service. Under Augustus, this usually meant they would get land.(the money rate was roughly 3-5 thousand Denarii, depending on the period) It was an excellent way of keeping soldiers content, and the beauty of it was it put satisfied former soldiers out on the frontier, presumably with the hopes that they could form a first response militia/raise the alarm in the event of an enemy attack.

In terms of reverence, the most significant thing to mention would probably be the Roman Triumph. A general who won a major victory would have a sort of parade known as a "triumph", essentially a celebration of their victory.

That being said, care was taken to ensure this didn't go to a general's head. IIRC there would be one person with the general on his carriage whose sole job would be to repeatedly whisper in his ear that all glory was fleeting. So success was absolutely celebrated, but they made a point to avoid letting military figures get big-headed. Which was a sensible thing to emphasize, given how trigger happy Roman generals could be about marching on Rome.