I strongly recommend taking Chill Touch or Fire Bolt as one of your two cantrips, because the EK is generally bad at ranged combat. Chill Touch may deal 1 less damage overall, but it's just as good at stopping regeneration and fewer things are resistant/immune. Ray of Frost might be alright, but the range isn't good enough IMO. You can use javelins if within 30 ft, especially if you can use extra attack (your DM may vary on this, as by RAW you can only draw 1 one your turn, but this is an oft ignored rule).
For your second cantrip, something for melee would be fine. Booming Blade isn't particularly good, unless you are attempting to tank. Green Flame Blade can be good, but don't discount Sword Burst in case you get swarmed (but beware if you have any adjacent allies).
Other options to consider, in order to optimize your use of War Magic, would be cantrips that use saves instead of attacks. Toll the Dead is probably the best for this, since it can deal 2d12 damage, but Frostbite can be good IF they fail the save. Acid Splash, Create Bonfire, Infestation, and Poison Spray also have their uses in this regard. Arguments could be made for non-damaging spells, such as Blade Ward, Minor Illusion, or True Strike, since you could use those every round as well, but you give up a good amount of damage with this option.
For your Level 1+ spells, I highly recommend that they mostly be situational spells, such as Shield, Absorb Elements, and Misty Step, since you don't have that many slots, and most damage spells you could cast won't be as good as a cantrip plus war caster attack. AoE spells should be your "go to" damage spells, such as Shatter and Fireball, to help against swarms of enemies. Magic Missile is a decent option as well, because it's auto-damage (which sometimes you really need).