Skyediver,
If you become over focused on a given goal you will find that your game[plan loses flexibility.
Study the various victory condition and make a judgement as to the victory paths that are feasible and those thar are not. Your choices will be based on:
1. Your personal preferences i.e. war or peace, trade or isolation etc
2. The traits of your leader
3. The type of terrain you occupy.
4. The location and traits of your near neighbours.
I find it best to retain as much flexibility as possible without compromising your goals. It is important to be able to react quickly to an ever changing politcal landscape.
Personally I prefer peace, trade, expansion (though not to rapid), science and culture.
I start the game by allocating 100% cash to science, getting 4 or 5 cities up and scouting out those very precious resources. I build a lot of cottages because I like lots of cash at my disposal. I keep costs low by funding a small military in the areas that I perceive as vulnerable, of course a unit or two in each city keeps the population happier, so I try not to neglect the military but I by no means overfund it.
Obviously the early game is very important, getting your civ of to a good start early on will prove more valuable than trying to catch up later. Almost always I avoid conflict early on and focus on building a solid foundation. However at times I have thrown everything at the war machine and overrun my neighbours before they know what has hit them, this is a dangerous policy, if you fail you have nothing! Your choice buddy.
The middle game is a time for consolidation, expansion, finding allies and making lots of money. I tend to place an equal emphasis on cash, science and culture. I still commit almost all my budget to science, build a lot of cottages and build lots of science and culture buildings. Keeping ahead on tech is important. My underfunded army can crush a larger opponent if I pit my cavalry against their horse archers.
I don't like sharing. If I share a large island with someone i will foster a good relationship with them an plot! When the time I right I will push them into the sea and keep all their former cities for myself. I try to blitz such a rival and take them down as quick as possible, say 10 turns or so.
The end game requires great care, keep a very close eye on your rivals and above all keep as many victory paths open as possible. It is important to watch ALL your rivals, even the weaker ones can surprise you. Be ready to address any rival that even hints at going for victory. Stay at peace when possible but be ready to pounce if a rival is getting ahead. Spies can be very useful at halting production of say the United Nations or Apollo Program. Spies are also very good at cutting off a rivals access to resources.
Keep a close eye on rivals by using your non military units; spies and missionaries etc.
If you keep many victory paths available and check the progress of your rivals then victory can be yours!! GOOD LUCK