I'm sorry to welcome you here.
Some toaster ovens and combination microwave/convection ovens have "drop down" doors that require less force to open. Some toaster ovens also have the rack that comes out when you open the door, which can be good or bad. I didn't see a countertop just-microwave with this type of door, though.
Otherwise, my guess is that a handle would be easier than a push button, because there are more options for opening it. You can add grippy tape or silicone to make the handle easier to pull. You could possibly tie on a pull as well, that you could also use a gripper tool with. You can use a stick for the push button, but that might take more leverage.
With one hand better than the other, and doors that typically swing one way, you'll want to make sure that the door you choose leverages your better hand in the space you have.
Of course, as Steve and Nikki note, you always want to look at controls. Apart from a touchscreen vs. a dial, some dials are push/turn and others are just turn. Also, a dial that has distinct clicks to reach settings may be more difficult to turn.
The Dycem mat that Fusia mentions is a great solution for stabilizing a countertop microwave, or anything else on the counter. Dycem is also good for couch/chair/wheelchair tables and trays to keep items in place.