The best civ abilities does depend solely on your style of play and what kind of map your playing on.
1. I prefer industrious, because the workers build so much faster, your city will grow and become more productive faster, thus countering any advantage of the other civ attributes. You can also connect your cities faster and access those luxuries quickly. Can save money by not needing as many workers to complete your projects. Also large cities get a bonus on shields.
2. Expansionism is awesome on a huge pangea map, I often get ALL of the ancient techs from goody huts, by sending out 4 or 5 scouts. Having Construction and having the choice of becoming Republic OR Monarchy, before most of the AI even has Bronze Working is a huge lead. I also get the whole earth mapped out so I know where to settle towards (resources, luxuries). However, on an island map, or tiny map, I would avoid this attribute because it's useless then.
3. The earlier comment about that France always seems to lose when controlled by the AI, this doesn't necessarily have to do with their attributes. In the Civ3 editor I noticed there is an area where you designate what each civ builds alot of, or never builds. France is checked off to build lots of happiness improvements, so probably falls behind in other areas (military, science). Also France seems to always attack me first (I play as America), thus provoking a war and slowing down France's progress.
4. Peaceful players shouldn't be to worried about anarchy, so religious loses some of its appeal. I rarely have to switch governments when I've been Democracy.
5. Science gives you 3 free techs the whole game, but does shorten the time it takes to build science improvements. Still not worth all the hype it's given.
So here is my list:
1. Industrious
2. Expansionist (on a huge pangea map)
3. Scientific
4. Religious
5. Commercial
6. Militaristic
7. Expansionist (on a small or island map)