The biggest problem with jack of all trades build is the lack of attribute points and feat points to invest into everything.
So here I'll give you a list of builds with the lowest attributes and feat requirements, as well as recommendations against some builds with heavy requirements. I suppose you can combine some of these low requirements builds into a working jack of all trades build.
For guns, shotguns actually have the lowest requirements: you can refer my 3 PER shotgun build here:
https://stygiansoftware.com/forums/index.php?topic=9661.0However, since you want to pass perception checks, a good candidate will be assault rifles, which only require 8 PER and a few feats. Another candidate will be LMGs, that build has more requirements, but it is possible to weave a sledgehammer into that build, allowing you to both melee and use a gun (LMG). You can refer to my Rambo build here on how to do that:
https://stygiansoftware.com/forums/index.php?topic=10948.msg43801#msg43801If you want even higher PER for checks, I suppose sniper rifles is technically doable at 11 PER and just a few crucial feats... but I have not tried any sniper rifle builds yet, and have not seen any guides that proposed any PER lower than 14. So take at your own risk.
As for PSI, if all you need is just utility and support magic such as stuns, immobilizations, and free adrenaline shots, then you can refer to my Paladin build here:
https://stygiansoftware.com/forums/index.php?topic=10486.msg42465#msg42465. That build has 5 slots for support magic, and requires only 3 WIL. If you need to be occasionally killing mobs with magic, then that requires heavy investment into WIL, the minimum I have seen is 11, from the Bloodpsican build:
https://stygiansoftware.com/forums/index.php?topic=8588.0 If you go PSI, you will definitely be getting Premeditation, which requires 6 INT to obtain. The 6 INT provides not much, but still decent bonus to your hacking skill.
As for Dex, 7 Dex is the perfect threshold, as it fulfills requirements for skills like Grenadier and Escape Artist, and it adds a decent bonus to lockpicking.
Avoid SMG builds so they require heavy investment into DEX, as well as at least 6 PER.
Avoid pistol builds as they require too many feat points, as well as heavy investment into DEX and PER to work properly. Unless you are talking about my stupid Gluck 17 pistol here:
https://stygiansoftware.com/forums/index.php?topic=8936.msg39405#msg39405Avoid knife builds as they require too much DEX and feat points to work properly.
In my opinion, sledgehammers for melee builds have the lightest requirements: I managed to get it working with 11 STR and no feats in my Rambo build.
Personally I will not consider Spears due to my bias for sledgehammers, but spears require investment into many different stats for its feats, that can fit well into a jack of all trades build. But still require many feat points though.
Actually, this can be fun to theorycraft, let me try to make one.