I didn't like Oblivion's use of minigames, in the end I just auto skilled everything I could. Talking to boost moods was just strange in the end, if I work out what a person liked and hated, I'd logically stop doing the things he hated and do only the things he liked. In the end trying to boost speech was extremely tedious, worse almost necessary.
Thankfully fallout's skill system is very much different to Oblivions gain per use system.
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I don't think minigames are necessary for Fallout if it's going to be using action points. I say this because I imagine locking picking, healing or some other such in the midst of battle. I'd like things a little more frantic in a gunfight, especially in a first person view. When talking about guns and such I think Deus Ex's approach would be much better then Oblivion's.
There were times where it was critcal to pick a lock to escape an area in the midst of battle and either stopping the game or stopping a person from lockpicking is much worse.
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If there
had to be minigames I'd like to suggest a system for medical healing, something similar to Metal Gear Solid 3: Snake Eater. Basically MGS's heal system involves going into a menu where it shows the protagonist's body with xray view and wounds. From here the game provides a description of wounds and what is required to cure it.
A poisoned bolt from a crossbow required:
A knife to remove the bolt
Antivenom to cure the poisoning
Styptic to stop bleeding
Disinfectant to stop infection
Stitches to close the wound
Bandages to finish
Now what happens is the health bar (normally white) has a red chunk displayed on to show how bad a wound is. Normally the bar will automatically heal to a certain point but red is a part that won't heal for a very long time. The more required healing supplies used the more the red part of the bar is reduced, if all the required elements are met then the red part of the bar is completely gone.
This 5 minute video demonstrates best.
YouTube - Metal Gear Solid 3 Snake Healing
It's a pretty fun system and quite fast, but I would adapt it for use with Fallout. The requirement would be to have doctor kits and medi kits and each kit contains better supplies (more of them too).
Now going into doctor would bring up a similar menu with a view of the protagonist and wounds. Now with a low doctor skill basicall it'll show the location of wounds but little else, high skill levels reveals the type of injury and further levels start indicating what is required to heal wounds. Curing injuries at high levels has chances of reducing or curing local injuries too.
Now risk is blowing the wrong materials on wounds (like trying to use antivenom on a broken arm), so it may be possible to guess one's way through things but ultimately costly.
Another possible problem is pattern memorisation, but logically a person would know how to do a basic healing after a while. Also high skill levels would result in more health healed anyway.
Finally I'd like to suggest Macguyver Perk! For use with repair, doctor and anything else applicable. Macguyver allows a character to substitute items or use less of an item to complete an effect. Having two ranks of Macguyver (max) means that some items require NO ITEMS to complete an effect.