(Trying to run a squad with SG-1-like technology, especially if you use limited numbers of troops, will get everyone killed. You definitely need advanced weapons and armor to survive reliably in XCom.)
Personally I keep promoted soldiers in the squad (until they die) - their improved abilities make it worth it, especially if you give them the better armor if you only have a limited amount.
There are three main ways to increase survivability:
1. Armor, starting with the standard armor, then moving onto power armor, then possibly the flying armor for some of your agents.
2. Research and build laser rifles for your troops, medkits, and then plasma weapons (plasma rifles, heavy plasmas). The laser rifles vastly increase your ability to hurt aliens. Medkits help survivability. Plasma weapons are better than laser weapons. Always use auto-fire (if you do the probability math to compare the different shot types, auto-fire works out to be the best for pretty much all guns).
3. You may want to check your soldiers' stats, and fire the ones with crappy stats. Of particular note is their bravery stat. If they have a low bravery, they'll panic easily, and you don't want that. The other really important ones IMHO are their reaction speed, and a hidden psionic-related stat, which you would need to send them through psionic training to unhide (so you can just ignore it safely until later).
Obviously this isn't a comprehensive guide to what to research, and I haven't told you in what order to research things. I've just suggested some things which vastly increase your soldiers' survivability.
You can manufacture and sell some items to make tons of money, for example: laser rifles. Or sell off extras of recovered alien stuff, such as alien corpses, or equipment or ammo that you don't need.
You may also want to try doing some things with conventional weapons in the beginning. For instance, I like having a couple guys with explosive or incendiary ammo in autocannons and heavy cannons.