I have won at monarch using something similar to this:
I build few warriors, then build settler, and in between spearmen and warriors. The warriors will be used to upgrade to swordsmen later on. Or if you want to use horsemen instead, build chariots.
In between build settlers, when cities reach size 3. I don't bother with culture so early. Build your cities so that they overlap somewhat.
After a few settlers are built and you have 5-6 cities, build granaries in some of your cities. Not all, because some will be used to build barracks and units. Once those granaries are finished, build settler-spear-settler-spear and so on, while the other cities produce spearmen and horsemen and barracks, and upgrade those chariot or warriors to horsemen or swordsmen and take out a nearby civ.
I usually can surpass AI in score and cities once I get those granaries finished. Before I'm usually somewhere in the middle.
Once you have gone some cities over the Optimal no. cities or there isn't any decent land left, which should be around near end of Ancient Ages, build temples or libaries (depending on which trait, if neither then build temples). Core cities should build both. Build marketplaces and courthouses in your productive cities, and you're ready to go for those wonders and wars in the Middle Ages.
I would use this strategy on a large map. If you decide to do the ancient war, then you should go up to 12-15 cities and then war. If you're going builder style, which is probaby better if you're not too good at monarch, then build 20+ cities.
I usally have 1 unit in my central cities and 2 in my outer cities. The units help in keeping happiness, but luxuries+temples should keep cities at an ok level of happiness.
Also if you go builder style, use Middle Ages, to build more improvements in your cities, and maybe a few wonders, and go to war once you get cavalry. I would build knights now and then, because I believe they are cheap in upgrading to cavalry.
To keep up in techs, research at 10%, but buy most of them, with the money you're earning. Also wait till the tech is really cheap, or buy from one civ and trade to another in same turn. Trading world maps also helps.