@EditorRex: you did not mention pottery for cottages? Much better for commerce than fishing, it takes only 10 turns for a cottage to catch up with a sea tile, then it just gets better. Build them as soon as possible and your finances go up by themselves ( slowly, but steadily )
My strategy after the rush depends. As mentioned in the article, code of laws and currency are good to have when you have so many cities (besides, there`s almost always more you might want to build)
In general, mathematics is nice - opens up some good possibilities like currency, or construction for more war ( see article - another way to get money is to simply conquer the next guy... )
If I conquer a religion, I tend to research priesthood, code of laws.
Code of laws is usually one of my first targets anyway - it is essential to reduce city cost, with a lot of cities, you can later get forbidden palace, and, if you are really quick, it might also get you that religion - on Prince level, that should not be too hard I think. Also, you can get caste system, which I like a lot because I tend to play non-creative, so building new cities becomes way easier - just use an artist, wait a couple of turns, be happy, instead of spreading religion or building a monument or generally investing hammers and thought
I try to avoid horseback riding by the way. It is quite expensive to get early on - so unless I want to use elephants, which I like, or have a UU, like carthage, I tend to ignore this tech until I rush with cuirasseers much later in the game.
In order to repair myself, I tend to get writing soon. That way, I can go to low tech rates ( happens when you have too many units ) and simply use scientists for researching the tech I need to get back on track financially. As a bonus, a great scientist or two appear. Those can be used for example to get Alphabet ...
As the cities I use for rushing tend to have food to enable them to use mines, they should also be able to build a library and then just get a scientist or two.
This depends a little on who you play, though, it of course works best for philosophical leaders.
And it is not a long-term concept.
By the way: I would choose if I were you - either macemen as the next attack unit or knights. I personally prefer macemen - slower, but they have city attack. And they get real nice later when you have riflemen - upgrade, riflemen with city attack - yay
And knights usually are not strong enough to get by without catapults anyway, which only move one - so, same deal. Also, opponents tend to get pikemen which can be really annoying, with macemen, this problem is not so bad. And: macemen require bureaucracy, which I like.
If my opponent gets knights ( they usually do ), I tend to counter with either war elephants ( if I get ivory ), or just defend ( I usually simply play nice, I don`t care to give a tech or some resource to keep the peace, again, religion works like a charm ) until I can get gunpowder and then military science ( great tech for liberalism ) later. Cuirasseers are my favorite rush unit later, because they tend to be the first strength 12 unit on the map and I usually conquer at least one civ with them when I choose to do so.
Well, hope that helped some. I tend to write too much, sry bout that