Here are some hints I can give about the differences between vanilla and RAR.
As an introduction, I would say that at the opposite of Vanilla, there's no reason to run for an early independence. From start, the Royal Expeditionnary Force is so huge that it's clearly a deterrent for any quick game. If you want to be able to pick up that fight, you'll need to grow big.
in the first turns, a big novelty is the shipwrecks of course. They can turn out very valuable as long as you avoid your early caravel to get killed by wild sea animals. Don't hesitate to explore shipwrecks even when you have a single boat as if you lose it, it will be replaced by the king.
Then of course you need to build your economy. Producing manufactured good is essential, and as in vanilla, sending settlers to get trained in native villages is very efficient to have quickly good planters. A useful tip, you can train several units in the same village at the same time. That's pretty interesting especially for farmers and fishermen.
Once you get enough schools and colleges, it is time to grow food like a freak so that your population growth would rely more on domestic fertility than immigration. I try my best to fill up all my schools, colleges and universities. Even basic schools deserve to get fill up as we never have enough farmers, carpenters, fishermen and lumberjacks. They all turn quickly overpriced in Europe. To grow food, don't neglect mills and granaries! They can change your life.
As we talk about city growth. Be aware that when you reach from 12 to 14 people, you will need a healer's cabinet. That's very important, because without health all your production, including food, could be reduced by 25%, which means your colony will literally starve. This can happen very quickly if you don't pay attention. The healer doesn't need to be a professional in the early stage, but you need someone in the cabinet.
Among the new ressources, don't neglect hemp. From hemp, you can produce sailcloth and rope which are very beneficial to sell in Europe (besides being necessary to build ships and chariots). In the same way, it is very useful at a certain stage to grow sheeps and cattle because of the food generated by the butcher. The issue is that cow skins and wool are absolutely worthless so you really need to produce quickly leather and woolcloth in order to make them a tiny bit valuable (at least worth the price of a trip to Europe).
Another thing is that you don't only need to produce tools to get the better buildings, you now also need stone (for some buildings and units you can even need other stuff but I won't start on that). The good thing though is that RAR has a great trade route manager which allows you to automatically send your tools and stones in all the colonies that don't produce them. I personally dedicate specific chariots for that.
Later in the game, you will discover the domestic market. Once your goods aren't worth much anymore in Europe (because the prices have fallen), it can be interesting to distribute your goods within your own colonies. Do that only after checking that there is the demand for it. You can even import luxury goods from Europe and distribute them in you colonies demanding them. It can turn out pretty beneficial. To grow your domestic demand, you need markets and stock exchanges.
What I particularly enjoy with RAR is the fact that, the more it goes, the less you actually need Europe. And contrary to vanilla where you had to rush independence because you were getting unsustainable with the crazy taxes, here you trigger independence because... you just don't need Europe! With the domestic market and the custom houses, you have everything needed to get rich at every turn even without Europe.
A RAR game can be very long, but it's really a very complete experience. And at the end, you have a lot more the feeling that you've actually built a self-sustainable nation than you had in vanilla. That's why I believe it's really worth to dedicate many hours on it.