I usually completely forgo siege units until cannons. In some special cases where I have good access to enemy cities, I happen to build trebuchets. Siege units are simply too vulnerable and awful at fighting enemy armies to waste hammers and also frontline space on them.
And with tech choices, I usually go rather for science and culture, build a bunch of archers and when I have enough of them ready, I research the tech and upgrade my units. This way I save a lot of hammers (archers are much cheaper than CBs) and I have a quite useful army early on.
Moreover, you can train your archers against your worker farm, aka a city state. Move in with a group and just bombard without actually taking the city. It will take some time to upgrade them, though they will also be earning great general points. Just make sure they stay alive.