I wasn't going to post this until I had a bit more experience, but now I've got to. I started a ridiculously restricted game after spending 100+ hours as a massive hoarder, settlement-builder, and one-man-army. I just got really tired of play "Falloot" so this is what I'm going with:
Dead is Dead
Difficulty: Hard
Equipped Restrictions:
1 melee weapon
1 handgun/submachine-gun
1 rifle/sniper
1 auxilary weapon (shotgun, laser or plasma, missile launcher, etc)
2 type of explosives (grenades/mines) to max 10 units
Wearing a power armor adds one slot for heavy weapons (Fat Man, Minigun, Gatling Laser). These can only be used when in power armor
Max in backpack:
20 Stimpack
5 meals
5 Rad-X
5 Rad-Away
5 of any combination drugs
2 changes of clothes
2 types of meat to max 10 units
1 weapons in the backpack (if it's not on the hotkeys, you can't switch to it during combat)
Only pick up caps and ammo, no junk. No or limited fast travel. Can buy junk/shipments at Diamond City when you own a house there. All crafting to be done at Diamond City. No building of settlements. Companions allowed, and can carry the same as you. Must be equipped by you with weapon and ammo!
So far I'm only 5 hours in but loving it. Having to decide if I want to keep that bottlecap mine or my 2 fragment-grenades, deciding if I should ditch the shotgun in favor of the laser musket, should I keep the leather jacket or don some metal? - decisions, decisions... Finding that modded out rifle will be all the sweeter when it's difficult to get your hands on by yourself.
I went with
Strength: 2 (I'm not gonna carry anything, and armorsmithing will have to wait anyway)
Perception: 3 (Only need lockpicking as I tend not to use VATS that much)
Endurance: 9 (Yup)
Charisma: 3 (I was unsure wether or not I wanted the option of lonesome wanderer. Decided I did)
Intelligence: 6 (Aiming to get nuclear scientist)
Agility: 3 (Sneak to avoid mines and of course enemies)
Luck: 2 (Fortune-finder & Scrounger)
It feels like hard is a good setting. You can still get mauled pretty heavily in a bad situation, but all-in-all it should be manageable. Reduced access to mods will keep your damage and survivability in check.
I'm expecting this approach to hit some sort of wall as the content scales out of what I can keep up with, due to lack of items and modding, but I'm willing to give it a shot and see what happens. I also know it removes a lot of what is fun with the exploration in Fallout 4 (and I did have a lot of fun with it). But I got tired of playing the wasteland entrepreneur & freight-train, so now I'm just a Wanderer 