These are the tools which I use (mostly don't use) to build model kits:

Scissors Only used for some generic tasks such as cutting open plastic bags etc
Poly cement Melts the plastic and used for connecting two parts together firmly.
Mask An essential safety equipment when dealing with chemical vapors. Try to use something that ACTUALLY FILTERS.
Safety goggles Safety equipment automatically get the maximum score because they're essential.
Paint Brush I have 3 basic types. A narrow hard tipped brush, round thin brush and a flat large brush. If you want to paint using brushes, these three are probably the 'must have' ones.
File set Used to file down seams. Although it doesn't really get much use, it's still good to have around.
Sand Paper Preferably 200# to 1000#. Used mostly for getting rid of seam lines and scratches.
P Cutter A specially shaped hobby knife. Good for reinserting those sanded down panel lines. Not really a necessity, but then again, it's good to have around.
Cutting Mat A mat to cut things on, preventing scratches to the work surface.
Nail Clipper A efficient and cheap alternative for the plastic nipper. Also comes with a file!
Masking Tape Used to cover parts to prevent being painted. I try to avoid this as much as possible but painting some parts requires it.
Hobby knife The blade is significantly sharper than average craft/cutter knifes. Good for adding small details to plastic.
Air compressor Necessary for airbrush Used to supply air to the airbrush. I already had one before I got an airbrush. It's pretty noisy but it's only on for a few minutes.
Airbrush I have a double action airbrush called the 'Tamiya HG spray work'. I personally haven't had any experience with any other brushes so I don't know how this brush stacks up against the others.
Pinset Used to hold the decals and masking tape when applying them. This prevents oil and particles of dirt from your fingers getting onto the sticky side.