As far as not knowing the enemy for the first time - I've seen that and it usually goes down that way with the first fight being a beating. The PCs ran into some ghouls recently and took some serious hits before they realized what was going on. However, that depends a lot on the campaign. If you have mostly random bad guys every session, then yeah, they can't ever "be prepared" but we've got a vampire intensive story arc spinning up so that rules out the surprise them all the time technique.
And those common enemies haven't realized the PCs are a threat yet? Why haven't they contracted out to mortal hitmen, applied political pressure through their various contacts in the mortal authorities or hired supernaturals with other weaknesses to pit against the PCs?
Remember the denarians kept those viscious
attack dogs.
The red court has a lot of sway in local politics.
Etc.
The bad guys don't actually prefer a stright-up fight, remember. They only do that if they think they can win.
I like moving away from an inventory intensive "catch" bag though and the idea of spending FP that you suggest seems on the right track. However, once a PC says they have an "Iron Sword / Blessed Sword" etc. it's hard to tell them they need to spend FP to use it. That starts breaking down into details I think the FATE system was trying to avoid, but IMO the catch system leads you in that direction. I definitely prefer declarations and FP (and really think the enchanted item slots and stuff are going in the wrong direction) and want to find ways to keep that going.
But keep in mind, the DV is a real world. Carrying around piles of artillery or deadly weapons is likely to create all kinds of serious consequences. Players can't just saddle-up with
every single catch-satisfier they have every time they go out on the town.
Maybe I'll switch them to have an aspect of "Blessed Bullets" which had free tags on the first fight and then require spending FP for them, or declarations to renew it for future fights. Works great for Ammo, not so great for swords though.
This is a workable solution.
Keep in mind, if a player has an aspect, it allows trivial declarations be made for free. The "Blessed Sword" that one character has means he likely has access to it unless unusual circumstances (and a compel!) prevent it.
Not everyone should have the "Blessed Sword" aspect, though. Then it stops being unique.