If you have access to a research library, Broughton's prosopography, Magistrates of the Roman Republic is the starting place. It comes in two volumes, organized by year, and lists all the known magistrates for that year as well as their Pauly number (more on this later). It also provides an index by name, and lists all known magistracies a particular guy held.

The Pauly number refers to an encyclopedia entry in Pauly-Wissowa's Realencyclopädie der classischen Altertumswissenschaft. That book is a pain in the ass (especially if you don't care for 19th century German), but it's going to have everything we know about just about anyone you care to look up, and will tell you where to find the ancient sources for the dude. There is an open access version of this at [Wikisource](Realencyclopädie der classischen Altertumswissenschaft).

There is an abbreviated English version of that generally known as Brill's New Pauly. There is a searchable online version if your library subscribes, and the physical book is much easier to manage.

As you know, Romans didn't have a huge number of names, and those Pauly numbers make it easy to distinguish between different members of the same family with the same name.

That's what a professional would do. I don't know what to do if you don't have access to a research library and are intimidated by the German.