Please note, I'm not an expert card/paper crafter. The 'essential kit' is MY opinion only. If you have a different opinion on what is essential, please feel free to share. I love learning and if you post some of your tips, it could benefit everyone.
The things I don't think I could/should do without are:
Sharp things - scissors, craft knives and scalpel,
Sticky stuff - double-sided tape, glues and glue-pens,
Measuring things - rulers,
Cutting platforms,
Card
Receptacle for the stuff you throw away.
I haven't shown my full collection of sharp things - I don't use all of them in my crafting - I have a good collection of dressmaking scissors that shouldn't be used for paper.
A scalpel is better for the fiddly work than a craft knife because the blade is precise and less bendy. Large scissors are great, but for cutting fiddly 'fussy cutting' as it's called, you really need a delicate pair of sharp, accurate scissors.
Sticky stuff for making the pieces of card stick together so there's not a collection of bits in the envelope when you deliver the card is also essential.
Glue can distort the paper so choose carefully. I used craft PVA glue to start with and it takes a while to dry, it is way too wet for some jobs and it's therefore been hefted from my essential kit in favour of smaller bottles of tackier glue with more accurate nozzles.
I also wouldn't be without the glue pen. The one I use is this, the Quickie Glue Pen.
Used wet, it sticks permanently. Delicate and fiddly bits can be stuck because of the easy applicator. If you apply the glue and allow it to dry, it then becomes a tacky glue dot that can be removed if necessary.
Measuring things - Please note, I'm not always a measurer. I use the rules for cutting against rather than measuring. The steel rules have been stolen from @s0u1 - his garage is so full of stuff, I doubt he'll notice they're gone. Even if he does see the rules on my desk, he'll never recognise them, they're now clean!
I have two cutting mats (blue and green) and I borrowed a plastic chopping board from the kitchen - if I promise I'll return it, it's not theft, right?
Card, paper, envelopes, card blanks, inserts, backing papers, etc etc - don't worry about all those things yet, just the bare essentials is all you need to make a card.
Last but by no means, least - I have two waste bins. This one -
and a box under my desk. The box is convenient for scooping all the card off the table, straight into it so I can keep the desk and floor clear, as well as being sure if it does get thrown, it goes straight into the recycle bin.
My last essential piece of equipment is not so easy to come by.
A room that you can retreat to when you want to immerse yourself in your crafting. Mine is my attic. I can close the door when I've finished and my craft stuff is not cluttering and littering up the whole house - because, believe me, it spreads and you have no idea HOW things got strewn all over the living room.