using sony 2100 and memorex 2400's. both seem to work fine. and about equal on life. so y'know... brand does count for something.
most important things:
NICAD:
(-) lower capacity
(+)they can take faster charging
(+)they can take faster discharging
(+)with a good charger life can stretch to well over 2K charges before notably degraded
(-)some older cells can suffer from "memory effect"
(+)Cheapest cells/chargers
NIMH:
(+) Higher Capacity
(na)Average charge speed
(na)Average/high discharge
(na) good charger can see >1K charges befor they start to degrade
(+) little incidence of "memory effect"
(na) more expensive cells + charger
LiIon:
(+) Highest Capacity
(+) Very Light
(-) Dont abuse them when charging
(-) Dont abuse them discharging
(-) Life span ~500 cycles / 3-5 years whichever comes soonest (from date of manufacture!)
(+) No Memory Effect
(-) Orribly expensive
(-) Very Very Rare
(-) Not all devices can use them
(+)Devices that can will notice - faster flash charging, faster zoom, brighter light (torches - at the expense of bulb life), longer run time, better cold weather performance etcetc
Choice of cell depends on application:
For digicams and most similar items (walkman, desk toys, cordless phones etc) NIMH is best - it will work, its a good price, you will notice the extra capacity
For very high current applications (RC Cars, Cordless Drills etc) NICAD is best - it will work, it will survive
For specialist applications (not excluding high current, eg RC Airplane, Hybrid Cars, Mobile Phones, GPS, Emergency Lights etc) LiIon - where max capacity, low weight, high energy density, cold weather performance, low self discharge
So for your dad, id say nimh. pick a decent brandname, energiser has been recomended above
and get what suits your budget. a decent charger can make the world of difference!