Are you using the default civs? Or are you modding in ones that don't exist yet...
Is it ancient era (Ie. start with basic units (settler + warrior/scout)), or is the world based around a certain time? (EG. 1000 AD)
If it is ancient era, and using default civs, PLEASE don't use the most 'popular' civs, as no matter what you do, Rome will always rule the world, if you be "realistic". Simply because, if you don't play as a european civ, the european resources will be depleated (IE. one civ will get horses, another will get iron, another two may get copper, and the rest go without). The only way around that would be to put tons of resources in Europe (like the Earth 18 civ map ATM), which means that anyone who can rule the Ancient era, rules Europe, and thus, tons of resources and production/trade/science/GP powerhouses of the world.
Try and spread the civs out as much as possible. This may mean you will only be able to fit 4 or 6 civilisations in Europe... but thats better (IMO) than the unbalanced Europe in 18 civ Earth maps given by default.
My 2 cents. But you need to give a bit more info about what "Importance" means, and what civilisations count, and what don't. Otherwise, no-one will be able to help you. Also, its slightly dangerous this sort of thread, so I would reccommend that you impose certain rules ("No replying to other peoples posts directly, explain your choices," etc. (The first rule is important, otherwise you get:
"X is a great civ"
"No its not"
"Yes it is"
"Ur civ sux"
"U suck"
"Ur mum sux"
"*8*($&(#$#*&)%(*&# u &#$*($&#)%*(#&(%*#&%"
etc. etc. etc.)) Or not. Its your thread, but if the mods think its going to end in a flame-fest, they will close it.
Now thats my 4 cents