You are aware that NiCd is no longer the preferred chemistry for rechargeable batteries, are you? For one it suffers from the so called "memory effect", second Cadmium is a substance that poses health hazards. NiMh or LiIon is the current state of the art.
You should provide a voltage regulator between the battery and your electronic circuits. Not many electronic circuits tolerate the varying voltage from a battery. Erratic an unpredictable behavior can be the consequence.
however... NiCd can generally provide more peak amperage than NiMH, and is cheaper than LiON.
so, at least in the US, they aren't really dead yet. they are one of the more common battery types for lower-cost cordless power tools (with LiON being more typical for higher-end models).
decided to leave out a longer description in favor of being more compact:
PbAc: lower cost, high current, low (useable, *1) capacity
NiCd: lower cost, high current, medium-low capacity
NiMh: medium cost, low current, medium-high capacity
LiON: high cost, medium current, high capacity
LiFePO4: high cost, high current, medium capacity
*1: the actual raw capacity of lead-acid isn't particularly bad, per-se, however only part of the capacity can be used without causing damage to the cells. if drained too far or left discharged, the battery may be effectively destroyed. in contrast, NiCd and NiMH are much more tolerant of being discharged and/or left in a discharged state.
approximate best per application (values relative to price):
small device, high current: NiCd, LiON (ex: power tools)
small device, high capacity: LiON, NiMH (ex: consumer electronics)
large device, high current: PbAc, LiFePO4, LiON (ex: engine starting, back-up power)
large device, high capacity: LiON, NiMH, LiFePO4 (ex: robotics, *2)
*2: both LiON and NiMH seem roughly break-even in a capacity-vs-price sense.
for a custom-built high-capacity pack, NiMH is cheaper. for premade batteries, LiON is cheaper.
for similar capacity, the NiMH pack would tend to be bigger and heavier though.
a drawback for LiON is that they have a risk (if not charged/discharged safely) of going into a thermal runaway and catching fire and/or exploding (LiON packs generally use built-in controllers to make them more-or-less safe).
could be wrong, this is mostly based on observation.
if the goal is to make batteries by hand, than NiCd or NiFe (nickel-iron) should be easier to make.
commercially made cells though generally use sintered plates, and using plain metal plates results in much worse performance. so, much beyond proof of concept, it is probably much better to buy batteries.
NiFe mostly differs in that iron-oxide is used instead of cadmium.