Linseed oil is probably the best option, considering cost/effectiveness. Don't use boiled linseed oil, that has solvents and things in it.
Sometimes handles have a plastic coating to seal them. You should just scrape this off.
For the first time, it's good to use a brush to apply the oil. You want it to really soak it up. Give it a good coating a leave it to dry. If parts dry quicker than others top them up.
I've seen places recommend wetting the wood, or leaving it in the sun first, to get it to soak in easier.
Once or twice a year (do it when the weather's nice) you can reapply some oil with a rag.
Leather Handles
I don't really know shit about leather.
The only leather-handled tool I have is one of those Estwing hammers.
They're made from leather rings (and a few plastic ones).
The original protection on the leather is shellac.
I've seen people online use neatsfoot oil on the leather. Apparently this is used for baseball gloves.
Other things I've seen are leather conditioner (like you might have for shoes), beeswax, animal fat(!), even linseed oil.