Unfortunately there's no simple answer to any of these questions. The term "modeling" embraces a huge variety of activities; the tools that are essential to one form of modeling are irrelevant to another. If you want to build large-scale wood models of sailing ships from scratch, you probably will need a table saw, a planer, and at least one lathe, in addition to a set of hand tools including chisels, carving tools, saws, etc. If you're into radio controlled, operating models, you'll need some electronic equipment that I couldn't begin to describe. If your primary interest is flying model aircraft, you'll need to be able to work on gas-powered engines. Etc., etc.
For the moment, though, let's assume that your interest is twentieth-century ship models based on plastic kits. (That assumption may be completely off-target; if so, please forgive me.) The list of tools and materials for that sort of modeling is actually pretty short. I'll pass on the advice that's in almost every decent book on the subject: start out by buying the stuff you really need, and acquire more as you need it.
The essential tools, in my opinion:
Some sort of knife. (Xacto or equivalent, with an assortment of blades - and enough duplicates that you can replace them when they get dull.)
Some good paint brushes (Check out the modern, synthetic-bristle assortments sold in arts and crafts stores. To my notion they work just as well as the legendary red sable brushes, and cost considerably less.)
A pin vise and an assortment of drill bits, nos. 60-80.
A 6" or 12" ruler, with divisions down to 1/64" marked on it.
At least one pair of good, accurately-made tweezers - preferably one with sharp points and one with blunt ones.
A set of small files.
A few sheets of fine sandpaper (check out the black-colored, super-fine stuff at a homeowner's store.)
A package of emery boards (drugstore-type).
A couple of foam-plastic-backed sanding sticks. (You can buy them from the hobby shop, or at the cosmetic counter of the drugstore for considerably less.)
Just about any sanding material will work on plastic - that is, it will remove the material. The best ones are those designed for wet and dry sanding. And (except in rather unusual applications - such as making major conversions) the finer, the better.
Some small clamps. (Spring-type wood clothespins make surprisingly good ones.)
A fine-toothed razor saw.
If you're going to get involved in aftermarket photo-etched metal detail parts, you'll need at least one small set of needle-nosed pliers, and a set of small side-cutters will come in very handy. (Several manufacturers sell tiny cutters especially for the purpose.
That should get you started pretty effectively.
If you stay in the hobby long you'll probably want to start thinking about power tools. A small hand-held "motor tool," such as made by Dremel, probably should come first. The smallest, least-powerful one you can find will be more than powerful enough for plastic modeling. (The ideal motor tool, to my notion, is one that can be set to turn at an extremely slow speed. Dremel apparently doesn't agree with me.)
I'll probably stir up some arguments because I haven't put an airbrush high on the list. My personal opinion is that, though airbrushes are nice, they aren't necessary for ship modeling except on fairly large scales. I'll go so far as to suggest that if you're interested in the popular 1/700-scale models, you don't need an airbrush. (The larger the model, the more big areas need to be painted, and the more helpful an airbrush will be.) My own interests are sailing ships and 1/700 warships. I use my airbrush about once a year.
Regarding adhesives - to start with, you probably need two: a liquid plastic solvent-type cement and some cyanoacrylate (otherwise known as superglue). Lots of varieties of both are available; each individual modeler has his/her preference. I personally like Weld-On No. 3 solvent and medium-viscosity CA (such as Zap-a-Gap or Hot Stuff Super-T). A bottle of "CA Accelerator also will come in handy.
Every modeler has strong opinions about paints. The manufacturers currently offer quite a few good ones. My personal favorite is PolyScale acrylic. When I can't get them (the nearest hobby shop that sells them is 45 minutes away) I used Testor's Acryl.
I suspect some other Forum members will jump in with additional suggestions - and disagreements. So be it. Every modeler has opinions about these matters. Fortunately, we live in a time when lots of high-quality tools and materials are available to suit a wide variety of tastes and interests.