I used to be really happy on Warlord, nice & simple! But After reading these forums a bit I stepped up to Regent, then straight to Monarch. I've just walked through my 2nd victory, so I'm going up again into the big leagues
I don't know the best tips, and I'm not that great of a player, but some of the things that really helped me are:
1) Republic - best gov't by a mile.
2) Losing my Wonder Addiction - I build Sun Tzu's & maybe Leo's Workshop, thats it until Theory of Grav & Universal Sufferage.
3) Knowing what you want from a city. - Often I used to build gran/temp/lib/rax/ch/etc/etc in all my cities, a little bit of micromanaging goes a long way.
4) Be line Military Tradition & Replacable Parts - War on your terms when you have these, and they don't.
5) Artillery - anything before it is crap. But 20 arties + 20 infantry rock.
6) Don't automate workers until you have so many that your nights gaming is just one turn of irrigating (thats not fun).
7) Most important C-X-X-C. It works. my last game I had 17% of the worlds land area and 35% of its population before I decided that the Iroqois deserved to die. They had 15% & 15%.
Just go for it...its not that tough!