So, I'm pretty sure the customs varied from time to time - I'm not an expert in the subject, so there might be someone with a better/more correct answer, but I'll do my best to answer it!

In "The Thirty Years War", Peter Wilson describes it once as "had to negotiate with the electors to secure acceptance. It was possible to persuade the electors to accept an emperor designate, known as the king of the Romans, who could assume power on his father's death. Otherwise, there would be an interregnum governed by the Golden Bull. This handed imperial prerogatives to the elector of Saxony in the north, and the elector Palatine in the south, while fixing a deadline within which all seven electors were to convene and select a successor under the direction of the elector of Mainz as arch-chancellor of the Empire. Candidacy was not open to all, since the emperor was not a kind of life president but a sovereign majesty, which presupposed that whoever was chosen would already possess certain 'royal' qualities."

Essentially, by the time that's covered in the book (~1600), Austria was by far the 'easiest' choice for the emperorship, being the most powerful nation in the HRE. There would be full elections, but they would generally elect the 'king of the Romans', the title that they would also elect to the 'heir apparent', to put it in other terms. There would be some political part to it (when he covers the 1611-1612 debates, which went on around the time of a civil war in Austria, some of the potential candidates get 'blocked' by electors - for example, Albert is blocked for being too closely affiliated with Spain). Candidates in this case were also backed by other nations, and political maneuvering to set them up or to change the backers mind seems also important.

However, as I mentioned earlier, it seemed like at the time it was fairly routine to simply elect the head of the Austrian Hapsburgs to the emperorship, and choose another one to be King of the Romans to succeed him. I can't speak as to the process earlier on, and this might be a bit threadbare for what you're asking - this is about as much as I'm able to easily find in this book, sorry :( Hope it helps though!

From a purely technical viewpoint, there were few requirements, as it was largely based on tradition and unwritten rules. Even the Golden Bull of 1356, which formalized the process, had no requirements for the candidate. Various written laws of the time would have rarely gone beyond stating that the person be male, christian, and usually capable of producing heirs. Writing down specific requirements would have seemed unnecessary at the time.

In practice the nobles of the Empire almost always elected the designated heir of the previous Emperor. These heirs were designated either the King of the Germans, or later King of the Romans. When there was no heir tradition dictated that the future Emperor come from one of the successor states to the Carolingian Empire, which made up the Electors of the Empire. Which states were Electors became more and more exclusive as the Empire went on. There was occasionally discussion about electing an outsider, as in the case of Edward III of England, but they never came to fruition for a variety of reasons. That rule regarding heirs ruled out the clergy and people in holy orders even if they were Electors, despite their proclivity for miraculously having heirs.