Makes a TON of excellent points.
My approach when encountering something entirely new to me is often more top-down than that.
It's the one that I recommend for parents, too-- because this way you don't waste a LOT of time chasing white rabbits down holes with things that aren't truly related to what you're after an understanding of. I start with review articles, not individual papers, no matter how fine or exciting.
Review articles:
1. Stick to BIG name journals, or those affiliated with major medical associations-- NEJM, JACI, BMJ, etc. are all good ones.
2. Pick recent review articles, or those upon which practice parameters (look to specialist medical association websites for some hints there) are based-- AAAAI and the like, in our case as food allergy parents, but you get the idea.
3. Read backwards in time. This gives you a sense of the timeline of research, and the HISTORY of particular researchers who are giants in the niche; it tells you who the big dogs are, and why. I also start to star articles that are "seminal" (that is, they recur in the review articles again and again in background sections, or in discussions of particular points)-- Pumphrey is one of those papers in food allergy research.
4. I second her advice to write down/look up EVERY word that you don't know the meaning of. I'll add that in medical literature, a working knowledge of Latin roots, prefixes, and suffixes is a major investment, but one that is more than worthwhile. Greek is also (less commonly) useful.