I have the same situation in Monarchy level, but I find Regent a relatively satisfying difficulty.
Now, most people will advise you go as a Republic... But due to quite a lot of AI's not caring wether you've been a good neigbour or not, Monarchy is - in my humble opinion- the better option. But that's also because I hardly play Religious civ's... Their bonus of having 1-turn-anarchy when changing government is good for an "adaptive politics" playing style.
Eventhough Economics gives access to one of THE best wonders, I'ld rather beeline to Mil. Tradition, because the cavalry is just awesome & it will be your main unit for a long time in the game. If you are coaxed into a war, you know you'll have the men to break their spirit.
When their initial assault has been pummeled into oblivion, then you just march your powerfull stacks (consisting of cannons, musket men, cavalry & the odd med. infantry) towards their doors, and you knock really hard
One of the biggest problems in this game is in how much corruption can cripple your empire. To counter this, being in a republic isn't the only way. You can tone down the corruption levels by building courthouses. Don't be skimpy on them, they'll save you tons of - well, everything. Build them in every city you have, no matter how small. (Though I'm pretty sure expert Monarch+ level players will undoubtely correct me for saying this - but on Regent it's not a bad move)
Other buildings like marketplaces, banks etc., you only need in cities with a 6+ population, as the return of those is too small in your tiny villages.
But most of all, don't be afraid to do some research trading. The AI's do it all the time between themselves anyhow, so you better do it too. Also, if you trade a tech with 1 AI, trade it also with the others you know, otherwise you'll miss out on whatever stuff those guys are giving for it - and which would go to the first AI you just gave it, because sure as hell he is going to trade it.
And while wonders are shiny and you want them as badly as Gollum wants the One Ring, they are not your main goal. If you do decide to build them, be careful which one to build though. The only wonders I care for are these:
- Sun Tszu's Art of War: free barracks until endgame, who could say no to that?
- Smiths Trading company: No upkeep for trade buildings? Ooooh ye$$$!
- Temple of Artemis: Eventhough made obsolete by Education, free temples that make your citizens happy & give you a cultural shield is nothing to shy away from.
These are the ones that are mostly on my menu, but the Temple is only optional, as it is only a temporary wonder.
Offcourse, the best thing of my strategy is that you don't have to be afraid of when a war is going to happen (and that's a given). And wars are good, because it will give you a Military Great Leader at a certain moment in time, with which you'll create an army. Once you have an army, you'll be near invincible - untill the others invent Flight. But with a bit of luck, by that moment, you'll have half or more of the planet all for yourself...