Roman politicians had a distinct career path, the cursus honorum. When Sulla had gained his dictatorship, he put his attention not only to reforming the laws, he also tightened the cursus honorum. livius.org gives an overview of the cursus over time, including the principate and the empire. The site does not mention Sulla's changes to the tribunate, which, however, did not outlast him by much. [Pompey, Cn. Pompeius Magnus, however circumvented all, and without any prior offices managed to get some form of imperium -- L. Marcius Philippus cracked: non pro consule sed pro consulibus -- to join Metellus Pius in the war against Sertorius in Spain, and on his return successfully ran for consul.]
Smith's Dictionary at Lacus Curtius has more on the cursus honorum and related posts:
quaestor
aediles (optional & potentially expensive)
praetor, propraetor
consul, proconsul
censor
princeps senatusinterrex
dictator (who had a master of the horse, wikipedia)
praefectus (see above cursus honorum for the various positions, most were created in the principate though)
tribunus militaris [Exercitus, pp503, 504.]
legatus
Sulla also put restrictions on functions assigned to the equites; however, like the tribunate, this too was reversed soon after his death.
