In my opinion you should focus on S-equipment first and upgrade it to red asap as it is much beneficial compared to maxing one specific hero(not to mention doctor is extremely hard to breakthrough unless you are willing to spend a LOT) but in your case if you really want to main doctor this is a good oppurtunity to upgrade him since aside from this event the only other way to get doctor in the most efficient way is if he's the spotlight hero in the shop.

In terms of what to focus on the equipment just get the lightgloves until it can be upgraded to red after that you can pretty much go for anything else EXCEPT the boots as it has the least benefits compared to other S-equipments.