Aslum's answer summarizes well. I'll just expand on the panic-level one:
Assuming that your mission is a success, then the panic level in the country that you visit goes down. However, the panic level on the entire continent of each country that you don't visit goes up (by two notches in the country in question, and one on the rest of the continent). This means that your choice can cause panic in a country that is not one of the ones that you are choosing between.
My normal approach is as follows:
Check the Situation Room, and look at the whole continents. Usually
I will choose the mission that will prevent any country from going
into panic. Early on in the game, specific rewards may be more
important. Or sometimes letting one country go into panic could be
better than letting four countries get to 4/5 on their bars - but
you get the idea.
If one country is going to panic anyway, evaluate which one to save on the basis of (a) Do they have a satellite already? If so, they may be a priority because I have no other way of lowering their panic.
(b) Would the loss of that country result in the loss of a continent bonus? If you have lost one country in a continent then the rest become less valuable; also, countries in your "home" continent are less valuable as they are not needed for the bonus. (Also, is it a continent bonus that you care about?)
(c) How much cash do I get out of that country? Losing a $60/month country is less of a blow than losing the USA or Russia.
If I'm not already decided by this point, then I'll look at the rewards. Usually cash is the best option, but early in the game it can be engineers, and if the squad is weak in the right area it can be squad members. However, note that engineers come in groups of 4 as rewards, and typically at the very start you need 5 to build an uplink. Alternatively, if all else is equal and your squad is struggling, it might be better to take an easier mission in the wrong place than to fail a Very Difficult in a better location.