I have a campaign centered around city-states that do not necessarily like each other. Is there an easy way to determine how many troops they have and what level their commanders have? How do I determine the value of their gear and how much access they have to magic?
As a standing army or a wartime levy?
Standing army is probably about 0.8% of the entire population. Keeping a standing army is expensive. Most of the military might of a nation will be conscripts, citizens, or a widely distributed aristocratic military class ('knights') which require some time to muster and organize.
Population of a city state is probably about 3-20 times the population of the city itself depending on the degree of urbanization. Southern Europe with its longer growing seasons was much more urbanized than Northern Europe, which basically depended on widely distributed substance farmers and needed a large number of villages to support each town.
In war, they might be able to temporarily mobilize about 10-15 times as many troops depending on the prosperity and militarization of the city state. However, its highly unlikely that more than 4% of the total population (5 times the standing armor) would be able to go on an extended campaign, simply because of the cost of that both in terms of the capital expended and the capital lost by depriving yourself of so much labor.
These numbers favor a short term stasis between city states. Even if you lose your army in the field, the enemy is unable to capitalize on that fact because you can always muster at least as large an army purely for home defense. Instead, wars between ancient city states are effectively about long term demographic warfare. The side that out breeds and out expands the other one eventually chokes its enemies off and assimilates its outer territories. The ability to out breed your enemy involves having stable social structures that promote large families, stable agriculture that allows for resistance to periods of famine and plague, and ability to resist cultural infiltration. A very good understanding of these dynamics can be gained by studying the wars between Rome and its rival Carthage, in which Rome repeatedly got trounced on the battlefield but Carthage was never able to capitalize on that and eventually Rome just grew too large for Carthage to continue fighting despite losing more soldiers than its rival. Rome's mono-culture more aggressively expanded than Carthage's loose multi-cultural confederation. Rome's agriculture proved more stable as North Africa experienced increasing desertification. The 'Roman virtue' proved better adapted to the technology level it found itself competing at. It was just better at turning out loyal citizen soldiers year after year and ground down its rival in a demographic war of attrition with the ultimate stake being basically genocide, at a cultural level, if not completely a ethnic one - although since victory usually involved killing all the enemies fighting age men, castrating and enslaving the rest, and capturing the women as slaves and concubines the difference between the two is a moot point.
Value of gear, access to magic, and level of their commanders will have campaign specific answers. Any answer I could give you in D&D terms would be wrong, because D&D has never had functional economics. If you read the 1e AD&D player's handbook regarding the economic situation it intends to simulate - namely, gold rush era Klondike Alaska - I think you'll see why without complete reform of the economic rules its silly to extrapolate from them. In general, the standing army will be well-equipped for its technology level, while the levied army will be variously equipped according to the prosperity and cultural traditions of the society. Rather than extrapolating what that means in terms of 'gold pieces' you are probably better off researching historical armies of different periods and matching that real world structure to your closest in game analogy. The prices of those weapons in the usual price guides are meaningless so no schedule of value can be set. For example, longbows aren't really expensive weapons to make - just expensive weapons to train to use.
Likewise, level demographics depend entirely on the sort of game you want to play. In my game, commanders are generally almost all between 3rd and 5th level, while leaders of nations and famous heroes might be 7th-10th level. In the Forgotten Realms, levels of leaders are at least twice that and its not unknown for entire units of rank and file soldiers to be 5th or 6th level.
And again, the availability of magic on the battlefield is even more campaign centric. In my game, there might be one 5th level combat centric wizard for roughly every 4000 soldiers in most armies. However, some cultures (elves especially) have relatively high numbers of combat wizards and that number could reach 1 in 100. Most standing armies in my homebrew are well trained to deal with wizards and will know about common spells with battlefield utility and how to combat a wizard on the battlefield. For example, heavy infantry will know to form shield walls to resist fireballs and other area of effect spells, light infantry will know to disperse, archers will focus fire on areas where they see magical activity, and skirmishers and light cavalry will be specifically tasked with harassing spell-casters. (Under my rules, this works, but it probably doesn't work that well under RAW, so consider the implications of RAW on the utility of standing armies if you are going to stick with it.)
You'll need to decide just how common magic items actually are. In a society that can produce wands of fireballs, lacks inexpensive effective defensive magic, and has magic item shops, standing armies as we know them from history probably do not exist simply because they aren't cost effective. Certainly a wand of fireballs has far more incremental military utility for the price than a sword +1, so if the rules allow equal access to them and make the wand cheaper than the sword, don't expect it to be logical for armies to have any soldiers in them in the traditional sense. You field 100 guys with mail, shield, and sword and I field 6 guys with wands of fireballs, then I probably win. It makes absolutely no sense to train and equip 1st level warriors with expensive hardware, horses an the like, if training and equipping 1/20th as many of wizards has lower cost and (much) greater battlefield utility. This implies that if magic is common, and works as in RAW 3.5, then the world can't remotely resemble history. Tier 1 classes certainly will defeat tier 5 classes. Military strategy will conform to the weapons and economics of the time, and if you treat the D&D economic system at face value there probably won't be any parallels with the modern world. Your best bet then is to ask one of your power gamers with high system mastery how he'd equip an army given the rules for a particular budget.