Hmm - it would help to see some examples of what you're seeing, since you should be able to use the priority system to something like 99% control what you get. (The only case being the odd ship where there aren't enough fleet points left for anything on your priority list.)
For weapons/fighters, this is a bit trickier.
1) You'd need to do more than cover small/medium/large in each size. For example, if the game is looking to pick a torpedo, a long range weapon, a PD weapon, etc, it'll prefer one of that type over another type that you have prioritized that only matches the slot - so you'd need to pick a wider range of weapons.
2) You'd also you'd need to pick some lower-tier weapons (which is more difficult since IIRC the weapon "tier" is not displayed anywhere. Basically, if you only prioritize Plasma Cannons, the game's not going to put Plasma Cannons in every single large energy slot; higher-quality weapons are not always "available" for a given ship fit, so you need to have some lower-tier options selected as well or it'll fall back to "everything" when the better stuff isn't available.
Stations are an exception here, iirc, with everything being available regardless of tier - so in effect they adhere to priorities more easily/strictly. But overall, for weapons, you probably need to have a wider range of things prioritized than you might think.
For ships, it's harder to say, but again it's probably not having some types of things checked - such as, say, a carrier, a phase ship, a tanker, a freighter, a crew transport ship. To my knowledge, this should work and let you select what ships you want to see, with the exception of the aforementioned "not enough points left so it picks something cheaper", which should happen fairly infrequently.
Yes, you are right. I seem to have forgotten that there is also a fleet budget the faction uses and that having blueprints unlocked isn't everything.
The blueprint-theme I'm currently prioritizing is some modded "woo look at this spooky experimental high tech stuff" ships&equipment, which might reasonably be quite expensive on the budget.
And I did actually notice that the stations had a way higher accuracy to the selections I made than most of the fleets, so that further backs up the budget maybe being the issue.
I was fairly sure that the fleet creator has more categories than just the obvious ones (separating longrange support missiles, short range strike missiles and torpedoes for example) but those are sadly not always obvious for every single piece of equipment (especially modded ones whose tooltips can include a custom 'category', or which may be very odd edge-case things due to cool custom scripts).
Sidenote (prioritizing freighters): How does this treat ships marked as "combat freighter" such as for example the hound? Will those only take up slots that would normally be taken by civilian freighters or is there any danger that the fleets start replacing real warship-frigates with hounds?
In general I'd never say that the system isn't good and useable as-is (it obviously misbehaves a lot less in a pure vanilla game).
However, it would be nice to eventually have a simple blacklist checkmark for specific things at some point in the far-off future.
Oh, and my deus vult luddic path campaign has taught me two things:
a) I want someone to make a LP variant of the Cathedral Hubship
b) It would be very neat to have hullmods included in the fleet design interface alongside ships/weapons/fighters, to make sure everyone's got safety overrides active on every single ship at all times.