if you want to tech upwards you'll have to do some of the following:
1. pick a civ that gets defensive bonuses rather than offensive:
-greeks
starting with demo for the 50% bonus is fantastic
starting courthouse means you get access to the best tiles
pikemen mean you can rapidly expand in relative safety (its hard to beat a fortified army of pikes behind a wall even with cannons)
-chinese
for the points mentioned already. definately geared towards tech supremacy
-japanese
your primary science producing cities are all going to be coastal. their bonus lets you grow those cities faster which leads to a higher rate of tech.
-india
the ability to use any resource can give you a HUGE leap forward if you start near dye. but this ability has a limited window of opportunity. still it might save you beakers if you don't have to deviate to a tech like monarchy
(if you're not going to run monarchy, or build the castle, and can already access dye you have no reason to research it)
-egypt
their free wonder means possible colossus or pyramids. either one would be fantastic.
+1 food and +1 trade from desert squares is amazing and further increased by a trade post.
personally I tend to go with one of the economic civs instead, and use my gold producing city to rush buy libraries and such in my science cities.
but there are some distinct advantages to teching as hard as you can:
1st to the majority of techs. learn which ones give you bonuses
I.E. you should go pottary, masonry, irrigation (unless you're against the egyptians) hopefully you'll get a free wall at your capitol and +1 pop in all your cities.
1st to catapults which at the very least denies someone else a free catapult
1st to invention so you can build the workshop while teching to rifles. this increases your defence on a HUGE level and if you have a tech advantage nobody is likely to stop you