Less important is the Capital One Cup with Chelsea taking on the 7th placed Spurs today. Tottenham Hotspur should go all out to win today, being eliminated from the FA Cup and a longshot for the top 5. Winning any piece of silverware is important for the Spurs, as they just exited the Europa League as well.
The Europa League remains important for relegation-threatened Everton. Advancing to the round of 16 last week, I think Everton should play most of the first team there and in the most EPL games while giving players rest against lesser teams such as Burnley.
The UEFA Champions League is the most prestigious club competition in the world but Arsenal and Manchester City find themselves down going into the away league. It should be pretty tough to overcome AS Monaco and Barcelona at their home grounds.