I would definitely recommend taking weekly lessons. You will learn a lot more in individual or two-person lessons over a long period of time than you will in a concentration/few weeks of a whole bunch of kids. Many kids at riding camps just go once a year for the heck of it, and aren't nearly as invested as you sound. If you want to take your equestrianism seriously, then by all means, get a personal trainer via weekly lessons. :3
Secondly, I think you have a great proposal to work at your neighbor's farm! After all, the greater amount of equestrianism takes place not from the horses back, but from his side. Go ahead and call them up or visit them to ask if they would need any help. Tell them what you already know well how to do (ie grooming), as well as what you are willing to work to get better at (ie stalls--hey, doing one well is a lot more complex than what us stall-muckers make it look like!). I cannot stress the importance of Asking Questions. It will gain respect from them, and actually makes you seem smarter than just going ahead and doing some thing that you either don't feel comfortable with quite yet, or that you simply don't quite understand. Over time, as you get in the swing of things, tasks will start coming naturally. Some other things you can suggest doing might include, scrubbing water buckets and troughs, picking pastures, cobwebbing, etc.
Just remember--no two barns do things exactly the same. So always ask if you're wondering why they do this a different way than your riding stable does...who knows--it might come in handy when you've got to make some of these decisions for your own barn some day. ;)
All in all, I think you are headed towards the right direction! Good luck, and keep it up! ^____^
~The Golden Filly!~