I think the first thing to say here is that there is no definitive list of what you should use and how you should use the tools you may have. We all have our own preferences.
If any list/lists are produced then they would have the caveat that the list and contents do not suit all cockers or all owners. We all have different preferences for different techniques and tools and for a number of different reasons. Coat Kings and stripping knives for example tend to have their supporters and opposers.
If you want a show trim then you will need to be far more aware of what you are doing, not just for now but for the long term. That's not to say you don't need that same consideration if doing a pet trim. Just because you have a pet doesn't mean you want any different a finish on your Cocker.
Then there are all the different types of coat, let alone the effects of neutering which will dictate what you can/can't do too - along with your and your dogs' lifestyles. Easy this isn't it
I would suggest that the basic tools are:
Straight scissors - for trimming the feet,
Thinning scissors - 42 or 46 teeth single sided - for thinning the feathering, ears, chest and head(pet only for the head)
Combs - fine tooth and woder toothed - also consider spinning teeth also. This would include a Spratts 76 but it doesn't have to be.
Matt splitter
Slicker brushes - find ones that are comfortable for you to hold. What suits one person will be agony for another.
For hand stripping:
finger stalls or latex gloves, marigolds, whatever suits you for gripping the hair
chalk again for gripping the hair
The more personal choice items depending on what you were looking for would include:
Coat King - 22 teeth
Clippers
Stripping knife
Stripping stone
Polishing mitt
Finishing spray - The Stuff, Show Silk or similar
But you need to look at the ranges available and decide what suits you, your Cocker and your budget - you can spend a small fortune on this stuff - often unecessarily