One should not perform any work before davening once alot hashachar (some 72 minutes before sunrise) has passed.[1] “Work” in this context is not limited to one’s employment, but rather includes a wide variety of household tasks of even moderate time duration.
The reason for this halacha is that when one gets up in the morning, addressing his Maker should be his first concern. Therefore, there are significant similarities in logic and halachic parameters between this restriction and those of not traveling, eating, or greeting people before davening.[2] Generally, an activity for the purpose of a mitzva is permitted before davening because it is not considered an affront to HaShem.[3] Even then, precautions are sometimes necessary to reduce the concern that one may get carried away and miss davening on time altogether.[4]
The initial reaction to your question is that neither option is ideal. It is best to daven with a minyan before working, and everything else must wait. However, in cases of significant need, the pre-davening restrictions may be waived. One classic example is traveling before davening when the travel arrangements will be unavailable after one davens.[5] (Not every trip justifies such steps,[6] but further discussion is beyond the scope of our present discussion.). The Ishei Yisrael[7] says that the circumstances that justify travel before davening also justify work before davening. These extenuating circumstances are also certainly grounds for missing a minyan.[8]
Assuming that you will not be able to both daven with a minyan and do so before starting work, your question of which of the two factors should take precedence is a good one. The consensus of the few sources on the matter is that it is better to daven first than to start working and daven with a minyan later.[9] The ruling is readily understandable. Under ordinary circumstances, it is forbidden to work before davening. In contrast, while davening with a minyan is an important element of tefilla and also makes it more effective,[10] it is not forbidden to daven without a minyan.[11] A serious inconvenience is a sufficient reason to miss a minyan,[12] and avoiding the prohibition of working before davening also qualifies.
That being said, the case for always davening first, even without a minyan, is not iron-clad. To begin with, the Rama[13] cites and does not entirely reject the opinion that one may do work after reciting Birkot HaShachar. Although we would not normally condone this, when it “buys time” to allow someone to daven with a minyan, it is not unreasonable. Second, those who have to daven very early in order to avoid working first may have to say Shemoneh Esrei before sunrise, which is permitted only under pressing circumstances.[14] If the minyan alternative has the additional benefit of being at or after sunrise, this might tip the scale in its favor. Finally, if the quality of the davening, from a practical or even psychological perspective, is enhanced at the minyan, this too is a major factor.[15] Therefore, we suggest that you discuss the different considerations and options with a rabbi who knows you and your situation well.