You've got a lot of opinions, some disagreements, and a few answers. Or an attempt at an answer.
I'm going to put my 2 cents in and try to add to the proceedings. First, my answers to your questions.
If I'm most interested in the ability to create progressions of notes that will sound "well", I should focus on learning scales, right?
Right. You are asking for validation in this question rather than direction, but scales should be learned. Chords are made from scales, and whole progressions can be derived from and fit into scales. Even when there are "out" notes, the majority of what appears in music follows this trend. The scale can be thought of as a basic part of our language; from it many things are constructed. You should keep a couple things in mind.
(1) Songs will modulate and the "scale" used may change; that doesn't mean that the previous statements are invalid, they apply to each new key (scale) that comes along.
(2) We frequently use accidentals to create more texture; this doesn't mean that the key has been thrown out the window. The basic structure is likely still going to follow the traditional key and scale with some deviation.
(3) When accidentals are used they are usually motivated by voice leading, creating a smooth chromatic movement on one or more voices. Common example is IV --> iv --> I, where the b6 of the key is introduced.
How important are scales in finding the right follow up sounds?
I don't know what you mean by "follow up sounds" but I'd say an understanding of scales and the chords that naturally fit into them is important for creating harmony and chord progressions easily.
Do artists mix scales in the same part of a song or do they come in order, as in one part is written using notes from one particular scale and the next part using notes from one another particular scale?
Both. In classical music one commonly encounters song structure that is in a well defined key for a section then modulates to a new key, perhaps a 4th up, then back down. And in some tunes a melodic theme may wind through more than one scale or mode, or even key in one section.
Is there something else to learn from music theory that would help me know what notes i could play next?
Yes, a lot.
Now here are some of my suggestions based on my experience. Some have stated that you should start here or there and mentioned a little theory. My approach to teaching is a little more holistic. You'll never win the chicken vs egg debate. You need to expose yourself to music and a lot of it. But that is not enough for everyone to learn the patterns that exist in classical western music and like it or not this has dominated the musical landscape for 100's of years. On the other hand you can't really learn music by only looking at text book information. So, I'd recommend you do both at the same time. The theory study will add to your depth of thought about the songs you play and the constant exposure to well structured music will enhance your understanding of the theory. By the way all theory books are written in SMN so there is no reason why you can't "play" your theory book and most state up front that you SHOULD!
Along these lines, the classic approach to harmonizing melodies is based on Church multi voice vocal music. While that may not seem relevant to modern music you might be surprised at just how strong the influence is. I would highly recommend going through a basic theory and harmony text. The virtue in my option is that (1) you start very basic using triads and that is easy to follow, and (2) you learn why certain combinations of notes and note movement work. While a fancy modern Jazz progression may seem to not follow, these basic patterns are actually embedded in the more complex chords and chord movement. Here are a few suggested texts:
Basic Theory - Harmony by Paulson and Cheyette
How to Create Jazz Chord Progressions by Chuck Marohnic
there are many more books available but I learned from these so I'm familiar with them. The key is to integrate the two forms of study. Again, PLAY YOUR THEORY BOOK. And analyze your playing and listening.