I feel for you. I have lunches with people from work and friends (or catered stuff brought in) probably about 6 times a month, and that doesn't include going out to eat with family occasionally.
First off, whether or not you get an appetizer should have nothing to do with whether or not your companion gets one. If they are insecure about eating an appetizer alone for some reason, that should be their issue, not yours. Same for having to wait to order. There are no rules that say you have to put your order in within a certain time period. It sounds like you are trying to decide whether to make it better for yourself or for them, but ask yourself who you are trying to take care of here. A lot of us ended up in the state we're in because we didn't put ourselves first sometimes.
One way I deal with the food choice issue is to try to look things up ahead of time. I know you said you don't always know where you'll go, but is it always new places? Over a couple years, I've amassed a collection of "go to" orders in most places we could possibly go. True, I don't always know the first time I go, but when I get home, I look it up online and know for the next time what I can order. Sometimes I just cruise menus / nutrition info of places we MIGHT go, and sometimes I suggest the place, or suggest three or four and ask which my companion would prefer.
Good luck; I know it feels like a juggling act sometimes. It will get easier.
And now that you don't have to be perfect, you can be good.