With the basic toolset you can make all models that are shown on this website.
I use a refillable 0.3mm HB pencil to make my drawings with. An wooden HB pencil is a good alternative but you need to keep it sharp with a good pencil sharpener. I would advise against anything softer than HB. The reason that I prefer to use a refillable pencil over a traditional wooden pencil is not so much the fact that it is more of an effort to keep it sharp but rather the fact that the graphite in the pencil shavings often finds its way to your model, making stains. If you prefer a fine-liner over a pencil make sure that the ink dries fast on the foam-core material as it will make stains otherwise.
I use a scalpel (handle no. 3) with a straight, pointy blade (no. 11). I prefer to use a scalpel over other knives because it is sharp and maneuverable. Other options include scalpel handle no. 4 with blade no. 26 or an x-acto knife. I find break knives or Stanley knives too coarse. What is important to consider when buying a knife is that the blades are cheap and easy to come by as you use many during cardboard modeling.
n.b. scalpels are sharp, very sharp: be extremely careful when using them.
I use an A4 size ‘self-healing’ cutting mat. I prefer not to use an old piece of cardboard or a piece of wood as repeated cutting will wear out the underground and misdirect the scalpel.
I use a very plain steel ruler of 30cm with millimeter markings. I prefer a simple steel ruler over contoured aluminum or plastic rulers because steel is durable and many aluminum and plastic rulers are not flush with the surface, making it more difficult to make precise cuts.
Set triangle or Protractor
I use a set triangle for constructing perpendicular lines and angles. Make sure to use one that has no protrusions on its surface, as these protrusions will dent the foam-core material.
I use a very simple compass. Use one that has enough friction in the hinge so that it creates true circles.
I use an ordinary solvent-based glue that sets fairly quickly. I prefer this glue over water based glues because it sets quicker and it does not cause the paper material to wrinkle.
Paper masking tape
I use a simple paper masking tape of 18mm wide. As the tape remains visible I always try to buy tape that comes somewhat close to the color of the foam-core material.
Double sided tape
I use a 15mm. wide, double sided tape that is normally used to attach photos to paper.
I use a 12mm. flexible and clear tape. I prefer not to use the matte ‘copier proof’ tapes as they are too stiff. Also, removable tapes are not usable in this context.
I use round toothpicks for hinges and such, not square ones.
I use silver and black pins of about 35mm. with a small metal head. Pins with a glass head are not usable.