With careful shopping, you should be able to fill this list with good-quality, long-lasting tools for less than $300. That's money you will probably make back on your first project or two.
A good power drill is one of the best investments most DIYers can make. It can drill holes and drive screws and bolts much faster than can be done with hand tools. If you think you will need the tool infrequently, you may want to buy a moderately priced corded drill. But nearly everyone will appreciate owning a cordless drill. Decent 12- or 14.4-volt cordless drills can be bought for $50 to $90. Look for a 3/8-inch model that either recharges quickly or comes with two batteries.
Research various types of cordless drills on Consumer Search.
A corded 7 1/4-inch circular saw is indispensable for cutting lumber and sheet goods like plywood. Avoid the cheapest saws, as they will be underpowered for some cutting chores. A good 15-amp saw can be purchased for a bit over $100.
Research various types of circular saws on Consumer Search.
A level is used to determine plumb (perfectly vertical) and level (perfectly horizontal). Levels come in many shapes, sizes and price ranges.
The most useful level is a 2- or 4-foot carpenter's (or spirit) level. If you plan to do a lot of home remodeling, you will appreciate having both. The best bargains have tough aluminum frames.
A 9-inch torpedo level is easy to store in a tool box and is useful for checking short spans. Do not rely on the accuracy of a torpedo level over long spans.
A 25-footer with a 1-inch wide tape will handle nearly every measuring need you have.
I've owned several basic, battery-operated Zircon models that have proven to be reasonably reliable with drywall walls and ceilings. On thicker plaster walls, I've often had success using the metal-sensing setting on the stud finder, which can detect the nails used to secure wood lath to studs.
I also frequently use a $15 Stud 4 Sure magnetic tool, which can quickly locate the screws or nails holding drywall to studs. You can have the same success with a few rare earth magnets.
See also DIY Stud Finder.