A good tape measure is the right place to start. Choose a tape with a longer "stand out", which is how far the tape will extend without bending, and clearly legible numbering and marks. Your next purchase in a measuring tool should be either a framing square or combination square. These tools allow you to mark out right angles, or "square" corners that are essential in carpentry. A level is also a must-have if you intend to build anything larger than bird houses. Levels allow you to plumb things and adjust them to be horizontally level.
First, hand saws are for pros. They require more skill and a lot more work to use. A circular saw is a good first purchase. It is more versatile than other power saws and will do most cutting jobs, with a little practice. A jigsaw is another good idea. They are more agile, with a thin bayonet blade that allows them to cut smooth curves. A router, table saw and miter saw are also handy items for the DIY carpenter that can be added as budget permits. A variety of chisels, rasps and files can be used for many shaping tasks.
Before buying nail or staple guns, consider a cordless drill, since a hammer can be used to handle nails and staples. Choose one with plenty of torque and higher RPMs versus buying the highest voltage you can afford. Larger batteries are heavy, and do not always deliver more punch. A pin nailer that handles pins up to 2 inches is a handy addition. Specialty joining items you might consider are a biscuit joiner, dovetailing jig for your router and a drill press if you do work that requires more than a few precision holes. A few bar and C clamps will take care of most clamping needs.
Preparation is more than half of a good finish, so start with a sander. A random orbital is one of the most versatile. They can be used on most surfaces and a wide variety of sandpapers are available. A belt sander is good for paint-stripping and heavy-duty work. Next to prep, the finish tool is most important. Use the best brushes you can afford. Choose fine natural bristles with a comfortable handle. Paint sprayers are good for lacquer, metal finishing and large quantities of paint. For smaller projects you may find you spend more time cleaning the equipment than spraying.