Sounds like a good start, make sure you maximise the size of your cities with aqueducts. There are some damn good wonders in Medieval, Sun Tzu's and Leonardo's are an awesome double act if you are going for military (any city with a road to your capital can a)produce veteran units; b)upgrade any units stationed there for half price as soon as possible!), Bach's has been great on every version of civ for happiness. Look to see which city has the most trade/research potential and go for Copernicus' and Newton's (and SETI later) in that city for a massive research boost.
You may want to consider changing to a Republic. If your cities are growing well and your unit support cost will not be prohibitive it is almost always better than monarchy. Compare the number of citizens you have with the number of units, if the number of units is larger (more than 50% larger with marketplaces) then you will probably lose money under a republic.
Given that you are maybe slightly ahead I would go for a science/wonder building strategy: Feudalism - Invention - Education (build universities everywhere) - Astronomy - Music Theory - Banking (build banks everywhere) - Economics then try for democracy. Make sure you improve land around 3 or 4 big cities so that they can get to size 12 and then move citizens to working on tiles with mines so that they can build wonders (you should do this with all cities, but it is especially important with wonder builders). Your cities wil probably be more efficient builders than the AI so you will be faster to the wonders. You may be able to use one wonder as a pre build for one that you want, for example start a city on sistine chapel and then switch to copernicus' when you get Astronomy.
Something military to consider... Cavalry are awesome if you can get them first and early, the increased movement and high attack are terrific. Bear in mind that they can go obsolete pretty quickly to rifles in cities so knights are advisable to build in advance ready for upgrading. For an all-out military game try going straight for Military Tradition and building the Military Academy so you can spend a while making Cavalry armies...
If a Civ has an agreement with another they are much less likely to declare against them.