A couple things in here I disagree with/have a different perspective on:
1. Archers are awesome! You always want a few early. I'd target 3-4 by turn 40. It's ok to delay other stuff a bit. Getting Archers isn't just about defense -- fighting barbs gives great return on investment. Completing City-State quests, recovering captured Workers (either for personal use or for more CS influence), stealing AI workers, etc -- Archers will actively boost your economy and pay for themselves before too long. Seriously, City-State influence is incredibly valuable, and Archers are the best way to acquire it.
2. On higher difficulties, you nearly always want to build Caravan before Library. You'll usually have time for both before National College, and an external trade route will be worth at least as much science as a Library AND will get you gold. I'm a big fan of super-early Caravans -- i.e., before turn 40. After the first trade route expires, then it's often better to switch to food routes. Food routes are very powerful, but you don't always have the spare happiness for them to be worth it in the early game.
3. Selling embassies depends a lot on the geography and the particular AI. Yes, giving an embassy might cause an AI to covet your lands, but letting them see your capital might also enable them to send you a trade route that would otherwise go elsewhere. If you don't think there's too much risk of them DOWing you, go ahead and sell the embassy.