Except that vmxa's point (it depends) is entirely valid. For example, I'll give my responses to your guesses, which will probably vary from the regulars' - and as an aside, I play as Regent-Monarch level, so that will change as you go up or down levels. Finally, "optional tech" usually refers explicitly the optional techs - the ones you don't need to research to complete an Age.
Bronze Working for Spearmen
Philosophy for free tech
Republic to switch to republic asap
currency to get marketplaces
Unless I plan to get IW early on for Swords or Gallic Warriors, I tend to wait for BW until later; unless you're doing a lot of defending, Warriors are better and cheaper. Philo-Republic I usually go for, but I don't usually expect to get Philo first - for me, it's more that it's on the route to Republic. Currency tends to be something I get towards the end of the AA; I much prefer Literature so I can start planting Libraries everywhere, as I normally play Scientific civs. EDIT: Also, if there aren't many Hills/Mountains around, I usually go for Archers so I have decent fighters.
Feudalism to get Pikemen and Medieval Infantry, might get for Sun Tzu's too
Gunpowder to get Musketmen
Military Tradition to get Cavalry
Either Economics or Music Theory for wonders
I almost completely invert this. I usually get Feudalism first thing, but then I beeline the upper path, turtling until I get Banks, then trade for the lower path techs. If I don't have a Cavalry UU, sometimes I completely skip MT (I have horrible luck leader-fishing). I don't often try to get Sun Tzu's unless I am certain I'm the first into the Middle Ages.
Steam Power for railroads
Replaceable parts for Infantry and Artillery and faster workers, and also for engineers
Motorized etc for Tanks
Flight for bombers
Electronics for Hoover Dam
Rails and then Replaceable Parts, although at that point what I get next is pretty academic. Scientific Method is usually something I go for soon afterwards, for the ToE, but I usually research the bottom path first just to get them out of the way and then go for Amphibious Warfare before Tanks and Planes. Then again, by the time I get to researching Tanks, I tend to be in a virtually unassailable position.
Computers for Mech Infantry
Synthetic Fibers for Modern Armor
Robotics for Radar Artillery
Again, at this point it's pretty academic, and this part of the game is the most heavily influenced by the WinCon (IMO) - are you going for Diplomacy, Space, or Culture? If so, you'll usually want to beeline for the techs you're going to need to get those (if you haven't already won a Culture, the Internet is probably enough to push you up). If you're going for a military win, it's pretty much preference.
