My problem with the jump was that I didn't escort my settlers or have adequate defense in my cities. I've since made it a priority to do both on Monarch.
I almost never sign a MP pact any more. I also make sure I have all my cities decently protected if I have a ROP pact. The AI likes to sneak attack (ROP rape) and if you have railroads, this can bring your empire down in a single turn. In one of my Monarch games India used a ROP & railroads to burn my undefended capital down to the rubble. That was the last thing I expected from my friend Gandhi.
I make sure I only fight a war when I want to fight one. In my last game as the Ottomans (Monarch), I fought my first war with swords, second one with Sipahi and the final one with MI/MAs. I cruised to a space victory in that one and had the option of Diplomatic victory.
Give in to AI demands (tributes) even though it might hurt your ego. There is plenty of time for revenge.
Don't break deals as your reputation becomes important in higher difficulty levels.
Trade with the AI often, especially techs and luxuries.
My wonder priority is in this order:
Great Library
Hoover Dam
Theory of Evolution
Bach's or Sistine
Leonardo's Workshop
I only managed to build the Great Library and Sistine Chapel from that list in my last Monarch game yet it was a fairly easy win. The wonder priority also depends on your playing style, victory conditions (UN, Apollo Program), civ & map. I usually play on large continents.
Pick the civs that best fit your style. I prefer relegious, industrious, scientific, agricultural & commercial traits (for C3C in that order).
Govts: I go from Despotism to Monarchy to Democracy. I normally fight short wars in Democracy if I'm not a relegious civ. If I'm a relegious civ, I may fight longer wars by switching to Monarchy if I'm fairly small and Communism if my empire if fairly big (large and huge maps).
This is of course what I do and prefer. Others do things differently (a lot of people like Republic for long wars) so it's up to you to find what works for you.