Normally, I initially have to use my NF point to boost Bureaucrats, in order to produce some positive cash flow. It doesn't matter how literate your pops are if your country is bankrupt. Once that's in the black, then I go for boosting Clerics to a MINIMUM of 2%, preferably closer to 4%. Be careful about overpaying your clerics, otherwise they start promoting out of that and into the upper class. You want them to get as much in the way of basic and life needs as possible, but not too many luxury goods.
As has been stated by others, the tech to improve research is important, as is the one to boost literacy gain through education. You may also need to research tax or administrative efficiency to keep the finances stable. Once I've got those under control and my pops gradually educating themselves into the 19th Century, hopefully before the beginning of the 20th Century, the next step is either military or prestige, because you can't neglect your army for too long without becoming a victim. You're not going to get necessary resources for your economy and pops without climbing the national rank ladder, and by far the fastest way to do that as an unciv is through Prestige. Navy depends on which country you play: if you're an island chain, you'll need at least some naval capability to defend your turf, but most countries can let that lapse for a while until they finish more important research. At low levels, basic small arms (firepower and defensive stats) and organization techs will benefit your army, but at higher levels, artillery becomes the dominant force. As an unciv, you may not get much benefit from artillery until late game, if at all.
I usually find it more reliably entertaining to play a borderline secondary power, or close to it. That's enough to arrange decent alliances, begin industrializing, and possibly step into the colonization race to grab a couple of pieces of land with badly needed resources. You're also within striking distance of becoming one of the lesser Great Powers if things go right. Playing as a smaller unciv too often leaves you at the mercy of events, and you can get annexed or chopped apart at a moment's notice with nothing that you can do to prevent it.