Other than having famous parents, if you were an ordinary joe (but of the right class) what was an easy way for you to get rich and famous enough to be elected a Roman senator?
What is the typical age of senators when they are first elected/chosen?
During the historical period there was pretty much only one way to become a senator, by election to a senatorial magistracy (the quaestorship or above). Senators appointed extraordinarily were not unknown, but they were extremely rare--pretty much the only way this could happen is to be enrolled directly into the senate by a censor or someone with censorial power (like Sulla during his dictatorship or the emperor himself later on). But one was not elected to the senate per se. The senate was an advisory body with few official legal powers, although enormous influence, and senators were not magistrates but ex-magistrates. One was elected to the magistracies and admitted into the senate after your year in office--like I said, it was the quaestorship which normally got you into the senate (after Sulla it was made a requirement, although emperors occasionally enrolled people extraordinarily using their censorial powers). The quaestorship had an age requirement, originally somewhere between 27 and 30, although it was reduced to 25 by Augustus. Originally it required military service, but at some point that appears to have lapsed--it was still traditional until the end of the Republic not to elect to the quaestorship someone who hadn't held a military tribunate, however. Eligibility for magistracy also had a wealth requirement, which varied but was generally 400,000 sesterces in the later part of the Republic--not an enormous sum, but not something that any barfly might hope to earn. One also had to prove before the citizen body as a whole qualification for magistracy--this means familiarity with the law, understanding of oratory, and the right connections. Novi homines like Cicero were thus rather rare. Cicero, like most candidates for political office, novi homines or not, entered into legal advocacy during the early part of his career. Such a thing was extremely common, as it established your reputation as an orator and legal expert, as well as (vitally) providing you with the connections and debts of gratitude necessary to succeed at the actual elections among the comitia. Cicero for example refused to act as a prosecutor until the in Verrem, and he was willing to take anyone on as a client during his early career as a defense attorney. Because of this he built up quite a lot of connections, apart from his increasing reputation as an extraordinarily skilled orator, and a lot of debts of gratitude, which helped him win a landslide election to the quaestorship at the earliest age. There were other ways as well, of course (Cicero's viri militares, for example, often served extended periods as military tribunes or promagisterially-appointed prefects before canvassing for the quaestorship, usually with the support of the promagistrates and magistrates they had served under), but on the whole some variation of Cicero's early career was the most common