I have two solutions for this: a blog, and Evernote.
I store my recipes online, on a Wordpress blog. Now, my blog is just for private use, so it's password protected, but I could just as easily make it accessible to the whole world if I wanted to do that.I have a mobile-friendly theme (design) installed, so that the content is formatted for a small screen when viewed on a phone.
With this system, everything is under my control, and I don't have to worry about what some recipe website does or does not let me do, or how some recipe site might change in future. (I have sad memories of a recipe site I used to love - they were great back in the day, but changed a bunch of policies and turned into an evil beast a couple of years later.)
Wordpress is pretty easy to use.
Another thing I use is Evernote, which is an incredibly handy thing. Go get a free account at their website, and put a few notes in your account. Then download an Evernote app for your phone, and you'll be able (with your password) to access (and edit) all your notes while using your phone. When I find some recipe I want to try, I copy it to my Evernote notebook, and then I can then access it while shopping.
I'm not sure if this is the kind of thing that'll work for you, but it's perfect for me.