The best saw for cutting your baseboard is a compound power miter saw. With this type of saw, you'll be able to cut clean, straight angles for butt joints and inside and outside corners. A simple chop saw or non-compound miter saw will not allow you to lay a baseboard flat and cut it with all the right angles.
Most baseboard molding is between 1/2-by-3 inches and 1-by-8 inches. Smaller baseboards can be cut in a regular 10-inch compound miter saw. If you're installing baseboards that are 8 inches or longer, use a 12-inch saw.
If you're purchasing a miter saw and you plan to use it for wider boards, such as 12-inch boards for shelving, consider buying a sliding compound miter saw. The sliding feature extends the cut several inches so wider and thicker boards can be cut. A 12-inch sliding saw is what professional carpenters and framers typically use to cut 2-by lumber for framing and decking.
Buy the biggest saw with the most features you can afford. You won't regret having a saw that's too large. But you could regret purchasing a small saw when you can't accommodate a shelving board. A saw with built-in lighting helps supplement light in darker places. Most saws come with dust bags that collect dust and help keep the work station clean.