Hello Odyseus, and welcome to Basschat from another late starter! The more experienced and the teachers among our fellow Basschatters will probably add their much more informed opinions soon, but my two pence is to forget about books and online lessons, and save up for even just two or three one-to-one lessons with a good bass teacher (not a guitar teacher who does a bit of bass on the side). That money will be the best bass-related investment ever, believe me, even if you end up deciding that it's not for you.
Playing with a pick is neither recommended nor discouraged. A plectrum will sound different from your fingers, and will suit certain styles and types of music better than others. If you find it easier to play with a pick, go ahead, obviously, but also get the abovementioned good teacher to show you how to play fingerstyle in an efficient, non-tiring way.
And my advice would also be to ditch the IMO horrid Vox headphone amp as soon as you can afford to, and get something more expensive but better (just ask here and you will receive lots of pointers to better equipment!).