In terms of extra curricular stuff, my school offers nothing, so I don't really know. I just visit as many galleries, museums and exhibitions as possible, either when I'm on holiday or whenever something crops up locally. Another thing that you could try out would be experimenting with different art media and sketching; you could even try and find a live modelling class or pottery class or something, or just go around galleries sketching. Gallery sketching is HILARIOUS. Everything I've ever tried to draw is very awful and dodgy, but it can be fun, and I think it helps you remember the composition of pieces better. Although I don't believe you require any artistic skill or talent to study (God knows, my own artistic talent is very, very limited!) HoA, I think experimenting can make you appreciate the sheer depth of the talent and technique of art better. For example, I'm obsessed with impasto atm. I've tried mixing paint with plaster and using different types of plaster based paint to try and build up texture, and I simply don't understand how people are able to create such detailed masterpieces (Like Rembrandt's self portraits, basically everything by Van Gogh) with impasto and thick paint; it's so clumsy, it's impossible! That's basically all I do as extra-curricular (Lol, does that even count as extra curricular?). It would be fabulous to go to lectures, student taught or otherwise, but I literally only know one other art history lover, and there's honestly NOTHING like that available to me in my home town. Most people don't even know what HoA is when I tell them it's what I intend to study.
In regards to extra reading, I've been trudging through Gombrich, "The Story of Art". It's fairly good in just giving you a solid grounding. Everything else I've read is basically junk my dad and I have plundered from charity shops; I don't even know if there's much I could recommend to you that's of actual academic merit. Listening to podcasts can be quite useful and also really relaxing. BBC "In Our Time" is phenomenal, I'm obsessed. There was a good one on Frida Kahlo released last July! I'd also recommend just searching for stuff you're interested in on YouTube, and watching whatever pops up. That can be fun; it's like Bertie's Every Flavour Jelly Beans, you never quite know what you're going to get! I'm also reading a book called "Thinking About Art" by Penny Huntsman. It was originally written as a companion for the AQA HoA A Level, but I've never had the opportunity to study HoA and feel quite disadvantaged, so I'm finding it useful in gaining a basic guide for analysing works of art. Huntsman provides a "toolbox" for what questions you should ask when looking at sculpture, architecture and paintings for the first time, which I've found to be immensely helpful. Generally, my "analysis" of Art is 100% personal opinion and interpretation, I have no idea what I'm doing and tend to say a lot of ridiculous and incorrect things.
I hope my rambling has been of some use to you! I'm very jealous of your experience with the summer school at the Courtauld; that would have been incredible! I visited during the summer and fell in love with everything there. Even Somerset House itself has such a strong historical presence; I think Cromwell possibly even died there? Idk. Good luck, hope I've been of some help! X