I only just finished Iunet, so I'm not that experienced, but I have found combat missions to be a lot easier than monument building missions (as monument building missions usually involve a lot more juggling of resources and trade).
The first thing that helps is reading the walkthrough sections, to tell you where each invasion is likely to take place. Afterall, if it takes you a long time to actually get your troops over to where the action is, you may be saying good-bye to half your city in the mean time.
Now, this helps with regard to how you actually fight the enemy. If you know, for instance, that the enemy will invade around a certain point, you may want to dispatch your troops to such a point to co-incide with the invasion. Why I say this is that there is usually a little period of time from when the enemy first appears on the map til when they start moving towards your city or troops. If you have a couple of companies of archers there waiting for them, chances are, you can do a certain amount of damage to the enemy before they even get themselves organised.
Another thing I found very useful was building forts and walls. I can't remember which mission it was (North Dashur perhaps?), but it was only a couple before Iunet. I had to fight the Libyans and the Bedouins. I knew where the enemy would appear, and I almost boxed them in with an L shaped wall, punctuated by many towers. Basically, once these towers were staffed, and the walls patrolled, I didn't even need to send in a company of troops, because as soon as the invaders appeared, they got cut down by javelin throwers and archers on the walls.
Walls and towers seem to be very good for this, as you can effectively direct where you want the battle to occur (otherwise, they have to go through the walls, and this never happened to me). Also, if you can bring troops from the sides, you can virtually envelope your opponents, which sends them running very quickly.
As far as troop choices go, perhaps this is because I have not encountered a strong opposition yet, but I've gone with archers. The reason for this is obvious. Firstly, you can start filling your fort(s) quickly, as infantry require all the hassle of getting copper to weaponsmiths, which is time consuming, as well as costly (because even if you don't have to import it, it's less copper you can sell, or more workers diverted from other industries). For the same reason, lost troops are more easily replaced. Obviously, archers are best from a distance, and in the earlier levels, you can pretty well just bombard the enemy before they get close. However, later, it is good to have an infantry company also. As mentioned before, towers and patrolled walls are of great assistance.
As for my method of fighting, well, I tend to do a bit of a point and click and hope for the best too. However, I have found that if my archers are there waiting for the enemy, they can usually do a decent amount of damage (perhaps it is good to mention the Academy at this point- yes, yes, double yes!). Then, I just go for the all out slaughter and try to mop them up with the infantry. I don't know, this will probably get me in some trouble later, but I find for now, I seem to be able to get away with only a couple of lost troops, which are easily replaced by the next invasion.
As far as setting up your military goes, invasions start pretty small, and get bigger with time, so as long as you build steadily, you really shouldn't have a problem. In land battles, build a couple of archer forts, and maybe one infantry fort. Obviously, there's no need to build more than one of anything at a time, since it will just sit around waiting for soldiers. However, it's good to have an archer fort while you're manning your infantry fort, as the recruiter will fill the archer fort if it's waiting for weapons to be delivered.
With water battles, you probably only need a handful (maybe as few as two, but I go for three) warship wharves to begin with, as the first invasion will be fairly weak. Also here, you're usually given a reasonable amount of notice (nine months at Iunet). So, even if you don't have any industries (dock, storage yars, shipwright, as well as wharship warves) set up towards building your fleet, there should be ample time to build your fleet, even if your shipwright is building some fishing boats.
Once again, the key is knowing where the enemy comes from, as this will allow you to be prepared, and allow your warships to seize the initiative. Your warships attack in certain priorities (listed in the manual). Basically though, the most important thing to know is that they will try to take out enemy transports first. So long as you are there waiting for them as soon as they appear on the map, they're not going to even disembark one troop. Unless it's a peculiarity of the scenario, don't even bother with transports yourself. Your warships should do the job.
Probably the most important thing with actually building either ships, or supplying forts with troops, is an efficient distribution network. This is important in all areas of the game, and no less important here. Make sure your source of copper is close to your weaponsmiths, which are close to your recruiter, which is close to your academy (it doesn't matter so much if the forts are a long way away, as the recruiter will continue to recruit, even while there are soldiers in transit, although, obviously, closer is better still). Likewise, make sure your source of wood (usually imported) is close to the shipwright. Warships will travel from the shipwrights fairly quickly, so it's not such a hassle if they're a long way from it.
As I've said, there's no need to start building multiples of everything immediately, as they will just sit idle. Another strategy to bear in mind, however, is using your overseer of the Workers. Particularly in naval missions (where you don't need to recruit), for most of the mission, your military will do very little. So, if you're running short on workers, switch the military to a priority of 9. Then, the month before the invasion, quickly set it to 1 (or whatever will fully staff it). Most battles (land or sea), are over fairly quickly, so even if this draws workers away from other areas, such as infrastructure, your city shouldn't come to a stand still, or burn down.
As far as the cost of establishing your military, once again, don't build unnecessarily. There's no use putting yourself severely in the red for three infantry forts, when you can only fill one at a time anyway. It would be better to stagger the construction. Also, key to the economy is a) building a reasonable population so as to b) support industry. Work out what your money crop is going to be. If you're lucky enough to have gold mines, you're pretty well set. Otherwise, work out what you need to produce yourself, or import, and make that your goal. There's no use setting up a an industry just to evolve your housing, if that's going to be to the detriment of your cash crop (don't under-estimate the power of taxation either). Usually, for any housing block, you're going to need a certain base number of inhabitants just to get the block on its feet. You need to set your Overseer of the Workers a priority early on. Obviously, there's little use in having a whole lot of jugglers patrolling around if you haven't even supplied water yet. Thus, max out each evolution of housing. Get to the point where it can't evolve any further, and then give them what they want. Provided your immigrants don't have to walk too far, you may even be able to cut what you've already supplied. For instance, if you need to supply entertainment, but don't have any available workers, cut health and sanitation, because by the time that has an impact, your entertainers should have arrived, housing should have evolved, and you should have plenty of new immigrants to make up the shortfall, before anyone notices that they don't have water. Then, once you've set up supplies of all the water, food, religion, and entertainment you need, and perhaps before, you should be able to set up industry, and start raking in those Deben.
I always find it does take a little while to set up my housing block to the point of having enough workers for industry, but once I get the ball rolling, it's fairly easy from there.
It seems to me that your problem lies in getting your housing block(s) established. As I have mentioned, not building unnecessarily, in conjunction with efficient distribution, and use of prioritising your workers should see your military nicely prepared.
Then, very importantly, it's just a matter of being punctual for the battle shorbe
"I am a railing beside the torrent: let those who can, grasp me! Your crutch, however, I am not."
-Friedrich Nietzsche