A lot goes into it and it usually ends up being a multiD decision but I'd say the general results are:
If its a CNS oligomet we usually treat that first.
For non-CNS and we really think its oligometastatic and possible to treat we usually do the primary site with definitive intention first and then go for the oligomet afterwards. I'd say we are most aggressive with breast patients, less so lung cancer patients who so rarely turn out to be oligometastatic (unless CNS only).
As an aside, our med oncs have 100% bought into checkpoint inhibitors enhancing the abscopal effect and we are getting lots of requests to try SBRT for melanoma, RCC, and now lung patients that we didn't use to see that only have a couple sites of disease. They are not really pertinent to your question because they usually don't have primaries at the time but its interesting how much that volume has picked up. Also very interesting having to say to a med onc "Im really not sure how I feel about using hypofractionation because I don't know the safe normal tissue constraints with PD-1 or CTLA-4 inhibitors." I spent so much time convincing them that radiation can be a useful tool even for metastatic patients that it feels strange to have them try to push us to radiate something.
As far as surgery vs SRS, that all depends on location and the patient. If possible, I like to consider surgery but very frequently its not an option.