Hey, I'm new to the site and Esperanto and I was hoping for some guidance about how to proceed in order to have the best learning experience. Will going through the courses in order be enough, or should I do the grammar readings first? Any advice welcome

Saluton kaj bonvenon!

Just start with the course, La teorio Nakamura, here. The course is available at many languages, pick one using the button at the bottom of the page. Every lesson has three parts: a piece of story, the explaining grammar and exercises to test, whether you understood the grammar. As you complete a lesson, the next one becomes available. Note, that you can retake any open lesson, but the scores from the exercises are for you only, I.e. there is no need to reset nor repeat until you get everything right. The explanations are usually very clear, and if you don't quite understand something, perhaps after next lesson the bulb goes on.

I recommend, that you take a look at the separate grammar part after a couple of lessons. And even then read only the relevant paragraphs, not the whole grammar part. Remember, that the lessons with their grammar sections will go through everything in much more digestive chunks.

Ask at the forum. Try to find a club or an event near you in order to learn speak. A summer course with a teacher from another country, so that you must communicate in Esperanto, is highly recommended.

Bonvenon al Esperantujo!