As red-swords go chrom is one of the worse ones. Lyn is good but overall agreement seems to say that ryoma/lucina/marth is the red-sword of choice, at least atm. Wait for ike later today though.
For lances, lukas is an amazing tank, while both catria and sharena are very worth raising. Imo sharena first since her supportive ability is better atm, catria is best used in flier emblem.
Out of your greys kagero is the best, so stick with her.
Focus on leveling and unlocking potential for now, leave skill inheritance for later, since it is very sp-intensive