Eldritch knight has 9/10 spellcasting, esoteric 5/10. Esoteric has a bunch of odd abilities, eldritch is a bare-bones chassis. They're not the same. Phantom blade is Wis-focused but esoteric wants to be Int or Cha-focused for those odd abilities which looks like a mismatch.
Anyway, ideas from a previous thread (4 of them mine, 2 David Knott's):
Fighter 4 / Psychic 2, as that gives you levels in the classes that are most usefully supplemented by this prestige class.
Paladin 2 / Exciter fractured mind spiritualist 4
- a variant on Cha to everything which the esoteric knight can push further with +Cha to AC via eldritch armor
Id rager bloodrager 5
- fastest entry. You get a lot more feats than bloodragers usually do.
Weapon master fighter 3 / swashbuckler 1 / slayer 1 / psychic 1
- lots of goodness from low level martial classes
Mindblade magus 7
- You've got most of what you want from magus and have a plan which involves many high-BAB prereq feats
Medium (Champion focused) 7
deuxhero mentioned taking a 2-level dip in it as a kineticist IIRC.
The best psychic class for the esoteric knight in my opinion is the archanist with the psychic bloodline. The one downside to using this class though is you have fewer slots to burn on the knight abilities. If you really want to use those a lot the scorceror is the best. Psychic gives you a good number of slots and still is dependent on inteligence. Whichever of these three you pick it's best to stick with a 9th level caster when going into a presitge class.
The best martial for entry is probably either fighter for feats, or paladin for fear immunity. Also of note is the ghost Rider cavalier for fear immunity.
Using your feats for presitgious spell caster is probably the most powerful build, but it leaves you pretty much the same as any other esoteric knight. You will gain all but 1 of the chosen class abilities, so there really isn't much variety there.
Re pure spellcaster entry; esoteric knight is a class which really isn't about spellcasting. You can force it with prestigious spellcaster^n, but it primarily improves martial abilities otherwise.
Fear immunity actually isn't that big a deal if you take the battle mind psychic esoterica.
I still stand by what I said before. You need slots to power most of the psychic esoterica, and you get the most out of increasing spell casting when you have a 9th level caster. Whether you decide to keep bumping spellcasting more by taking the prestigious spellcaster feat or not a 9th level caster is just better when entering a prestige class. The 6th level caster classes get other class features to balance out their weaker spellcasting. You give those up to take the prestige class, but get less in return. It's just generally a bad idea.
As to not needing fear immunity, it's still nice to have. First level slots might not be as valuable a resource to a normal caster, but to an esoteric knight they become a lot more valuable. Having to burn one each round to cast a spell will use them up quite fast. True you can replenish them with pearls of power, but if you have the fear immunity you don't have to make that expenature, which is especially useful when psychic casters are so easily shut down by intimidate which is almost impossible to avoid without having a complete fear immunity.
I feel like an Aether Kinetic Knight with 2-4 levels of Esoteric Knight for the Shadow Projection and Eldritch Armor seems really good. Sure you would lose some talents and infusions, but you get an extra battle buddy for a total of 2-3 and 2 extra feats.
Aether Familiar (Kinetic Whisper) no cost, Colossal Construct (Aether Puppet) 1 burn for 16-18 rds, and Shadow (Shadow Projection Esotherica) 2 burn for 2-4 minutes.
The Eldritch Armor works well with Kinetic Knight due to being able to focus solely on Con, to hit, and Cha. Artful Dodge, allows you to ignore Dex pre-reqs while still using a Full Plate; So you can focus solely on Str. Optionally, 1 level of Okayo Corsair lets you ignore Wisdom for combat feat pre-reqs. (Free glamered/Shadow is always good in my book).