The time period you are looking at is from Tiberius- Titus. You need to examine the way in which each of these emperor's used the military to achieve their own purposes. Don't forget that the praetorian guard is a part of the military. so:
Tiberius:
- Used the praetorian guard to eliminate any potantial threats- eg- Germanicus. The military was very poorly controlled under Tiberius, as Sejanus became the sole leader of the praetorian guard, which allowed for the brutal and unfair maiestas trials.
-"The emperor himself became tyrannical- or gave tyrannical men power. The cause and beginning of the change lay with Lucius Aelius Sejanus, commander of the guard..." (Tacitus.)
- Tiberius had a long military career before he became emperor.
- the riot in germany was quelled during the reign of Tiberius, by his nephew, germanicus.
- in AD23, soldiers were recruited from the provinces.
- the army began to play a role inside Rome. The vigiles became important, and had a role in the downfall of Sejanus.
- Sought to reduce robbery by reducing the distance between military posts.
- Avoided miltary action unless it was necessary.
- provided reliable military guidance, and built ties with the legions.
Claudius:
- Conquered britain during his reign...
- "And the britons beyond the sea shore which one sees,
Blue shielded Brigantians too, all these
he chained by the neck as Roman slaves.
He spake, and the Ocean with trembling waves
Accepted the axe of the Roman law." (Seneca.)
- Claudius was extremely easily influenced in his military commands.
- "Claudius fell so deeply under the influence of these freedmen and wives that he seemed to be their servant rather than their emperor; and distributed...army commands....according to their wishes." (tacitus.)
Had the loyalty of his troops- Scribonius tried to stage a revolt, but his legions would not fllow him, loyal only to Claudius.
- Cultivated his military image on Coins statues, buildings, etc.
- rewarded his troops with titles and grants of citizenship.
- Chose capable generals. The army was contented and well disciplined.
Nero:
- Was hugely influenced by Burrus and Seneca. Burrus was captain of the praetorian guard.
- "Seneca.....and Burrus, commander of the praetorian guard,...governed the empire between them....."
Had little interest in the soldiers.
- made serious mistakes in the choices of leaders.
- Killed some of the more successful generals.
This is not a conclusive, or even particularly comprehensive summary, but I hope that some of it helps you out.