Sooner or later you would want to wage war for one or another reason. Some countries are even guaranteed to be attacked by their long fought enemies, one example is North and South Korea who constantly breaches each others borders no matter what you do. For those time it's good to be prepared to retaliate.
Tactics: Use missiles to weaken them and rush their capital. If you take their capital, their military will surrender and the rest is just mopping up. Make sure the war is over in a week or less if you want to avoid the massive negative popularity from "war-mongering". Apparently it isn't war mongering if you win quickly.
Ordering military units: When you order military units, the game waits before they are all completed before delivering any of them. If you want to buy them quickly, buy smaller amounts from more countries.
I haven't been able to tell if there is any difference in the fighting effectiveness of different infantry types. It seems like career soldiers should be better than reserves or conscripts, but they aren't labeled differently on the map. The same is true for tanks and other military equipment form different countries.
Only countries with the corresponding military industry (tanks, planes, boats) can build military vehicles, and those are the ones you can buy from. Unless you are one of those countries, you can't build them yourself. But you can subsidize or exhonorate your military industries to get the ball rolling towards your own vehicles.
Nukes are used from anything that launches missiles, but you have to go through a bunch of politics first. In the defense department, there is a "law" that starts the authorization for using nukes. You also end up talking with your chief of staff. You get a specific code out of this that you need to write down (the game will not remember it). You then give this code back to the chief of staff when you want to use the nukes. When you select a missile launcher on the map, tell it to launch a missile. You get a choice of missiles. The nuke option is grayed out until you get political permission. Then just launch it like usual.
I haven't had great luck with using nukes successfully. As NK fighting SK, I successfully destroyed their nuclear power plant and irradiated half the country, but the air defense batteries around Seoul shot down my other 9 nuclear missiles. I remember another poster having this same experience (which is why I tried it), but I don't remember who. Also, the international community didn't do anything to me for trying to nuke SK 10 times.
I've never tried it, but my guess is that invading Syria as Israel is easier than others for three reasons: First, Syria's capital is close, meaning you can rush it easily. Second, Syria has terrorist groups you can fund, meaning you can destabilize the government. Third, it might be easier to find out some bad thing the head of state or country is doing in order to get UN permission, or at least have the UN back off after the attack. I think I remember reading an AAR, or at least a description, of someone successfully invading Syria, Palestine, and Lebenon as Israel. You might want to look for that.
- Nuclear weapons require clearance from your chief of army to use, by which point he will give you a 6 digit activation code. In my experience, every country that has developed nukes (or has stolen them from conquered nations) will have this option and to use nukes, just ask and you shall receive.
- Biological and chemical weapons (grouped together) are hard to access - you can't even bribe your chief of army into granting their use unless you get nuked first. However, a very small number of countries do have a chief of army willing to permit their use, even without bribes or a nuclear attack on you - these countries namely are Indonesia, Brunei and East Timor.