You can get a Bucket Organizer for a 5 Gallon bucket which is a great way of keeping your tools in one place and it is easily carried around.
Your tool box should contain:
Hammer (Claw type 16oz)
Nail Punch
Wood Saw
Tape Measure (20 Ft)
Pencil
Framing Square
Torpedo Level
30 or 36″ Bubble Level
Screw Driver with Phillips Head
Screw Driver with a Flat Head
Pliers (standard head)
Needle Nose Pliers
Wire Snips
Straight Jaw Tongue & Groove 12″ Pliers (referred to as a CHANNELLOCK®)
Straight Jaw Tongue & Groove 12″ Pliers (a second one)
Adjustable Wrench 8″
Utility Knife
Set of wood Chisels
Scraper/ Putty Knife
Stanley Surfoam Shaver
Caulk Gun (go for the better model $10/$30)
A few other things to have:
Spray Can WD40 (lubricant)
Spray Can Silicone spray (lubricant)
Wood Glue
Duct Tape
Electrical Tape
Teflon Plumbing Tape
Sandpaper assorted grit
Small tub of spackle
Tube of painters caulk (for your caulk gun)