Honestly, I would love to see a strong emphasis on home-made and bootleg weapons. I would love a Fallout game whose early game weapons are a mix of pipe guns, ghetto blasters, black powder guns, crossbows, bows and other primitive and scrabbled-together stuff. Imagine taking a Volley Gun, a pistol crossbow and a three-shot home-made pistol into a fight against a gang wielding junk lasers.
Bows, oh yeah bows and crossbows. With plenty of special ammo too. Bodkins, poison-tipped arrows, dynamite bolts straight out of Redneck Rampage, tranquilizer arrows, flare and flashbang arrows, perhaps even the legendary Atomic Warhead Arrow for the lulz (and yes, this should be as stupid as it sounds). Let's Oliver Queen the hell out of this bitch.
I would also love to see a revamp of Unarmed. I would love to see graples, elbow strikes, all sorts of kicks, sweeps, eye pokes, pressure point attacks (a classic of the time!), karate shops, weapon grabs, etc. Having a unarmed fighter fighting you in CQC should be hell, not some guy robotically punching you until you fall.
How come we can't use foot unarmed weapons? Gimme a boot with a knife on it, or maybe a rocket boot (goes well with a Jetpack too). Maybe a boot that works like a super sledge, storing kinetic energy for mean kicks.
Melee... I feel the lack of spears - small one-handed ones, large two-handed ones, tridents, glaives, etc. Atlatls would be so dope. Slings - c'mon where's the slings?! Such dope little weapons, don't understimate them, and you can toss grenades with them too.
Shields, I would like to see shields as an defense solution. Kind of a "disposable defense". Simple normal shields for the early game and such, to deal with melee foes, arrows and such. Of course, good guns would go right through shields. Maybe Riot Shields or some shield made of futuristic metal or plastic for the late game so we can Captain America this bitch up.
As for guns... I dunno. A proper machine pistol would be dope, just ridiculously innacurate spraying of bullets. I would also like to see akin to a Fallout equivalent of the SOCOM. Bring back Needlers and give us loads of chemicals to put into them, maybe a rifle version too.