Every readily available source seems to focus on the electors and on the big dynasties that were, in practice, always elected, but who was legally (or customarily) eligible to become Emperor? Was it anyone the Electors saw fit, even, hypothetically, a commoner? Did he have to be a noble? A noble of a specific rank? A noble with territories within the Empire? How about those that had demesnes both inside and outside the imperial borders? Could the Emperor be a woman? A child?
Theoretically, any man (women were not permitted to be elected as Emperor) could have been chosen by the electors as the next Emperor, however, while there were no strict limitations on who could be Emperor, there were absolutely major practical considerations that impacted who could reasonably be considered as a proper candidate. Namely, that due to the structure of the Holy Roman Empire, and the limited ability of the Emperor to gain tax income via the votes of the Reichstag, the Emperor would have to have the wealth necessary to carry out the duties expected of them. These duties were quite extensive, since they not only included maintaining the Imperial Peace and the various imperial courts, but also to defend the Empire against external threat. While there was some forces available via the Imperial Circles, the main body of troops for wars waged in defense of the Empire would have to come from the Emperor's own pocket. This meant that the Emperor would have to be of a certain degree of wealth and power in and of itself if they were to have any chance of carrying out the responsibilities on their own. This in turn limited the potential candidates for Emperor to the wealthiest and most powerful of the Imperial princes who could reasonably campaign for the position, or notable outsiders like the King of France.
In addition, while the Emperorship was an elected title, it was expected that a candidate for Emperor display a certain degree of inherent "Emperor-ness" if he wanted to be seriously considered for the position. In addition to the practical necessities of a pre-existing powerbase to draw wealth and military power from, being a noble of respectable wealth, prestige, and other intangible qualities were also in consideration as a showing of already possessing the necessary imperial qualities. This would likely exclude any potential commoner Emperors, since--by the virtue of not being a noble--even the wealthiest commoner would have been severely lacking in "Emperor-ness".
To summarise, while--in theory--there was nothing in the imperial constitution preventing any man from being selected by the electors as Emperor, practical and cultural necessities severely limited the pool of anyone who could be realistically considered. Any would-be Emperor would need to be able to draw upon their own resources to perform the duties of the position, and also demonstrate that they possessed “imperial” qualities already to be worthy of the title. In that respect, the pool of individuals who could be realistically considered was quite small. The large domains of the House of Habsburg in the southeast corner of the Empire made them one of the largest and most powerful of imperial princes, even before they secured an electoral seat for themselves as King of Bohemia, and this large powerbase was a major reason for why the Habsburgs managed to hold the imperial throne for so long: they were one of the few who could conceivably have the resources to actually be Emperor.
Hope this has helped answer your question and please let me know if you have any follow ups.