For a saw that can handle the curves, look for a good saber saw. Sometimes called a jigsaw, it has a small blade that cuts with an up-and-down motion. Look for a good-quality saber saw with a long stroke and about 3,000 strokes per minute. You can change blades to cut leather, linoleum, plaster, wall board, metal and hardwood up to an inch thick.
For more on power tools, consider:
Chain Saws 101
How To: Choose the Right Saw for the Job
The $20 Japanese Pull Saw: A DIYer's Best Bang for the Buck