i encountered once when i was only building my second or third city,roman empire immediately declare WAR on me....(i was using mongolian empire)i was shocked and his empire had more than 3 cities and his army was way too i must say to me at the start is quite a lot...and their tech was fast...i was playing chieftain level....
You mentioned that you like to improve your economy and focus on growth first
Maybe you made plenty of workers?
Maybe you built unnecessary wonders?
Maybe you built buildings that arent needed. Like Barracks in a city that doesnt produce much
Library and Monasteries in a city that isnt good for research
Built a stables even though you wont train mounted units
In this game, you really need to specialize
Look in the strategy articles section for "City specialize" or something like that
Here's a thread of mine about the same problem
http://forums.civfanatics.com/showthread.php?t=188932
Read those Analysis of traits threads too
another question,if at the start of the game, i always straight away make my settler build the city on the spot,but the surroundings is not very good,only have pig and trees...i was thinking at the start,should i find a better area to build my 1st city?
A pig and a few trees is decent, as long as there isnt too much desert, tundra, mountain tops, etc
If you're not satisfied with that, build a warrior or a scout and explore, the more you explore the better you can see your surroundings, and plan an expansion better
For me, I settle new cities in places with:
Rivers, a few floodplains, a few hills, grasslands, with a few forests
I try to stay away from places with:
Mountain tops, deserts, tundras, ice
spots surrounded by jungles <-- this is a bad spot at the start, because your city will have difficulty growing (because of lack of food, which can only be gotten if you have iron working, and chop the jungles, which use up too many workers/actions)