First are scissors  -  Pinking shears, the zigzag teeth, are great for giving a bit of detail, but not
necessary.    
A good pair of plain large blade that you keep solely for paper. 
A pair of fussy cutting scissor is essential, there are many types but as I have arthritis I find the spring assisted fiskars are brilliant.


Tweezers - again you can get different types flat nose and pointed.  I find that the reverse tweezers are amazing, though they do take a little to get used to.

Pokey Tool  -  Many companies sell these, whether you use and awl or a pokey tool they both come in useful for many tasks.  

Cutting Mat  -  Coming now in may sizes and colours you can get one to suit your craft.  

Score Board  -  You can get these in 6inch and 12 inches,  they allow you to mark lines into paper or card at regular intervals so you can make tidy folds.  They all come with a scoring tool.  I have a 12 inch score easy which comes with an extra piece to mark and help make envelopes.  

Cutting Tools  -  Whether you prefer a guillotine or sliding cutter having a good blade makes alot of difference.   I was lucky enough to find and xcut guillotine at a boot sale and I would highly recommend it.  

Double sided tape  -  They are in thick and thin widths, you can get a red tape which is plastic coated and very strong or white tape which works as well but can be torn when using it.  

Glue  -  This is a very difficult choice.  As a main glue you are best to try a few till you find something you like.   To use on fabric Fabri Tac is in my opinion the best one.  It is always useful to have PVA (School glue) on hand.  This can be used as it is or watered down to provide a base to work on or to protect your work when you have finished.


Paper  -  I mostly use basic copy paper there are also - Onion, Rice, Glassine, Greaseproof, Tracing and Watercolour that I have used.  I'm sure there are other I haven't found out about yet.
There are many other tools you can use, depending on your budget.  Die cutting/embossing machines, hot foil machines, Dies, Embossing folders, Stencils, Cricut, Xcut, Photocopier/Printer, Inks, Coloured Sprays, Glossy Accents, Punches, Corner rounders and so much more.