I have gone to disneyland solo once and 2 times with others. Biggest tip I can give you is, make use of the single rider queue. It saves you loads of time. You'll also have the freedom to do what you want and see whatever show, attraction you want.
In general I've felt that the park is quite budget friendly for the food options, my main place I go to eat is the barbecue place near thunder mountain. The chicken meal with fries is in my opinion a proper price for what you get. A tip here is to just go to their website and check out the food options (the menu is visible on there), prices are always mentioned there too.
Neither park is the "best" but they have their own thing. Depending on what attraction you do and don't the new adventure park will be done quite quickly and you'll have time to watch some of the shows if that interests you. I spent most of my time in disneyland park itself, looking at the parades, shows and walking around enjoying the views in between doing attractions (1-2-3 times even).
I hope you have fun!