You do need writing: it is a prerequisite for Literacy and it allows you to build diplomats, a very useful, early-game unit.
People have different strategies depending upon their overall approach: early conquest folks (who would probably better speak for themselves) would likely go for Monarchy, rather than Republic, as it's a much better early-conquest government (free unit support, settlers eat less, martial law, and it can be achieved faster than Rep.): Alp-CoL-Cer-Mon
From there, I think they head for Elephants: HBR-PT
On watery maps, Map Making will also be essential for transportation. Indeed, as one wants maps and transportation for almost all strategies, Map is essential, although I find that I can delay it in favor of more urgent needs.
I, like you (apparently) am an early-republic player. Entwined with that, I will also pursue Philosophy (Cer-Mys-Phil) for the extra tech advance (again, always nice, regardless of your strategy, temples and improved temples (both essential for an early republic at high levels).
Once I have an improved government (i.e., Republic), I am always aiming for Trade: BW-Cur-Tra. This enables two of the best early wonders (Colossus and MPE) and the best unit - the caravan (until Freights are available, anyway).
Once I have Trade, I head for Astronomy, for Cope's in the SSC: Mas(trade for it)-Mat-Ast.
From that point, you have a lot of options, so I'll shut up and let someone else opine.