Do I need to pick just 3? This is a team that's mostly young and ascending, so it stands to reason that they'll just keep getting better. I'm going to reword the question to - "who do I think on the Rams is on the brink of a breakout year, where they go from being just a guy or someone who can be taken out of the game or someone with glaring weaknesses to being someone who is feared by the opposition".
On D, I'm going to cross Aaron Donald, Robert Quinn, Alec Ogletree, TJMcDonald off the list because they've already broken out. Their continued ascension is assumed. Guys like Chris Long, Laurinaitis, Hayes have hit their ceiling, just hope they don't regress (with age). Guys list Rodney McLeod and Sims are already overachieving.
On O, I'm going to cross off Roger Saffold, Nick Foles, Jared Cook off the list for similar reasons. Cory Harkey is already overachieving.
Rookies just don't count unless they have superstar potential (e.g. Gurley).
The list of remaining candidates, folks who have a huge gap between potential and performance, is large:
O: Greg Robinson, Brian Quick, Tre Mason (**), Tavon Austin, Kenny Britt, BJones, Bailey, Lance Kendricks.
D: Baron, Janoris, Joyner, Tru Jo, Gaines, Brockers
That's my list in likelihood order of who I think WILL have the MOST significant breakouts. If I have to pick just 3, I'm going all offense, that the defense is already on the cusp of something great, and the D will be great even if the players mentioned just keep playing as is.
That is, if we see breakout years from Greg Robinson, Brian Quick, Tre Mason (**), that'll give the team a bigger push than anything else.
** - ok, I'm cheating on the Tre Mason pick a bit. In my mind, the Tre Mason pick presumes Gurley, that I'm thinking of them as a tandem act. Their breakout in my mind means that they get to 1600+ rushing yards between them with 4.5 ypc.