How do I securely mount heavy geometric reclaimed-wood shelf on plaster walls?

[Larry8]

I'm trying to personalize my new apartment on a tight budget with some DIY home decor projects, and I'm currently attempting to build a large, geometric wall shelf from reclaimed wood, but my joinery skills are admittedly novice. I've got the basic frame assembled, but I'm unsure about the best method to securely attach it to my plaster walls without causing major damage or having it collapse under the weight of books and plants. For fellow DIY enthusiasts, what are your go-to techniques for mounting heavy, homemade shelving safely? What type of anchors or fasteners do you trust for plaster, and do you have any tips for ensuring the piece is perfectly level when you're working alone without a helper?