oneshotcoy,
Well, if you "don't have to shoot a big trophy, but it would be nice" does that mean you will take the first legal buck you see but hope that its a trophy?
There are many types of hunting is SE Idaho, from an easy "meat hunt" to hard core trophy. If you go to the easy area you better shoot the first legal buck you see. Hunting in the rougher area's where there are big bucks may discourage you from shooting a small one.
I would suggest that you review the regulations, get a good map and drive around this fine country we call SE Idaho and get an idea of the area then ask some more specific questions.
Many of the "spike only" elk area's offer a good experience (not as many hunters and lots of elk) and would be a good meat hunt. Some of the "2 pt only" deer area's offer the same thing.
There are deer and elk in every unit with tags available. Research the country, call the local fish and game, and keep coming to this site!