Since you are playing a Fighter (EK): take the Alert Feat
Spells Known of 1st-Level and Higher. You know three 1st-level Wizard Spells of your choice, two of which you must choose from the Abjuration and Evocation spells on the Wizard spell list.
The Spells you learn at 8th, 14th, and 20th level can come from any school of magic. (PHB, Eldritch Knight)
Some general points before we get to specific points; if you can't find a better spell than FF, taking it can be handy, but other party members may be able to use familiars as well. Share the scouting responsibilities, or double down and take FF anyway. Familiars are fragile, albeit useful.
Familiars are not guaranteed to perceive dangers.
As you noted, some of the familiars have nice perception scores/passive scores.
Tactical note regarding scouting: the familiar may be detected by a hidden enemy while it is scouting, perhaps betraying the party's presence and giving the enemy a chance to strike first.
Owl, Bat, or Weasel can detect stealthed enemies for you. It can also be used to scout ahead and prevent ambushes.
Yeah, they are great scouts in my experience. But...if the enemy rolls higher on their Stealth check than the passive Wisdom(Perception) score, or the Wisdom(Perception) check of the familiar, the enemy can still achieve surprise / stealth. The bugbear is a nice example.
Skills Stealth +6, Survival +2 / Senses darkvision 60 ft., passive
Perception 10 / Brute. A melee weapon deals one extra die of its
damage when the bugbear hits with it (included in the attack).
Surprise Attack. If the bugbear surprises a creature and hits it with
an attack during the first round of combat, the target takes an extra
7 (2d6) damage from the attack. (MM, bugbear).
Alert prevents this. If you are a front liner, that's important for your build.
Alert is always on
Since you don't have to roll to prevent some problems, Alert is stronger for your use case.
Bullet two is extremely valuable for preventing surprise. Surprise can massively swing a combat - particularly if the enemy has numerous attacks, crowd control spells, breath weapons, or numbers.
Advantage on an attack roll against you increases the chance of a critical hit on you from about 5% to about 10%. Particularly at low levels, critical hits can be encounter ending for a given PC. Since you are the front liner, keeping your HP resource up matters to your group. Alert is very good for your role in this party.
While I personally like having the boost in initiative, I've seen arguments that the swinginess of the d20 roll mitigates that benefit somewhat - and you may not necessarily want to go first.
But as a front line warrior? You going first more often will usually help you with "the best defense is a good offense" for your team. Alert makes you a better front line fighter. While you may get an attack or two in with advantage when using a familiar to help, they are fragile and in my experience die quickly in battle if they get too close to the fray. That problem will vary a bit from one DM to another ... and how they run NPCs and Monsters.
How much sneaking around and ambushing is in the campaign?
That will inform which may serve you better. Your instinct to leave FF to other PCs is a good one. Find familiar is a favorite spell among casters for a lot of good reasons, but any class, spell caster or not, can take the Alert feat.
I find Alert to be more universally useful, so I'd recommend that if the choice is "either or", given that you are feat budgeting, take Alert, not Magic Initiate, since you will get spells as an EK.
But I need Hex for damage boost with multiple attacks! Feat choices
Now we have a feat budgeting issue rearing its ugly head.
Warcaster for spell casting in combat? Check. Great choice.*
Resilient Wisdom? Great as you get exposed to more spell casting NPCs/Monsters. Since I don't see a cleric in your party, this may be needed since Bless or other spells boosting wisdom are not available.
Magic Initiate? For HEx. Good choice.
Alert? Good choice ... but if you are running out of ASI stat choices, you may be better off doubling down on FF: you and one other with FF means "help" for scouting by familiars. Better chances to find stuff, but no boost to initiative, and no surprise prevention.
What come out is that FF or not isn't the hard choice, it's which feats, and when, and which ASIs.
Are you working together to build the party, or showing up blind?
The above considered, it comes down to taste and the kind of "feel" you want for your character. If you want to have both options, that free spell (FF) and Alert makes you an even better scout. But as a team player, letting one of the other party members be the scout could fit your party's needs better. Talk to your party mates and see what they think.