Here is a list of tools I could not live without!
Compound Miter Saw
If you plan on doing a lot of larger trim work you will want to invest in a
12" compound miter saw.
Brad Nailer/Staple Gun (with a range of 1"-2" Brads) & Air Compressor
A good drill
Cordless drills give you a little more freedom, but you do have to worry about batteries and charging them.
Corded drills are more powerful, but you have the cord to worry about.
Sander (small like a palm sander or mouse sander)
I like the mouse sander because the design makes it easy to get into corners.
Tool Box Tools: (in order appearance)
Hammer, 4 in 1 screwdriver (has 2 sizes of each head, flat & phillips), tape measure, crescent wrench, chisel, wire cutters, pliers, all purpose razor blade knife, sharpie, and pencil.
That's a good start for acquiring tools. For us it was a slow process. One tool here and there whenever we has some extra money. Also we took advantage of Harbor Freight Tools. Very low priced tools that got the job done. The funny thing about starting your tool collection is that when ever I give a tool to my husband for Fathers Day, Bdays, or Christmas I think he wonders if his gift is for me or him!