Adding to user37496's answer as I have some immediate (in)experience here.
I'm a beginner and in a similar spot: I've been playing for about three months, and I've included finger picking from close to the start. I don't feel that's been a mistake, and even at my level I can finger pick interesting enough music to keep me charged.
The basic concept of finger picking is straightforward. The mechanics aren't significantly more difficult than any other guitar part I've hit yet (no weird stretches!), and there's much less raw memorization needed than chords, scales, or notes.
There are some subtleties of hand position that I wasn't able to pick up from books and videos. I strongly recommend live instruction
As user37496 suggested, isolating the pieces is helpful: my chord switching isn't good enough to focus both on chords and on a new picking pattern, but I can hold a single chord while drilling a picking pattern, then swap focus and pick a simple pattern while practicing switching chords.
As far as learning resources, I started with a few videos, a stack of library books, and Mark Hanson's The Art of Contemporary Travis Picking. I was able to pick up decent open chord forms while I was arranging a teacher, but my picking hand position was off and I've spent weeks unlearning bad habits and concentrating on the right position. Going back I can tell that I wasn't holding my hand the way the book or videos suggested, but the difference was subtle enough that I didn't see it until it was pointed out. Now I can hear when I fall back on bad habits.