KiCAD comes highly recommended, but I went with the free CircuitMaker and haven't regretted it. It has the limitation that most of your designs have to be public, and while it has most of the features of the full Altium Designer, some of them are obfuscated by a simplified UI. That said, I've found the package to be comprehensive with some annoyances (like user submitted footprints that don't match the part), but I've made a couple dozen designs and revisions and generally think well of it.
There are certainly a ton of options out there, basic stuff will get you the files you need to mill, etc, or send to a fab on your own, but PCB specific packages will also get you supplied part footprints/pinouts, electrical checking based on your defined schematic, design and production rule checking, and much more. You can get really a staggering amount of capability for free, and actually fabbing a board is amazingly cheap.
The basic flow is:
Make your schematic from your chosen parts
Define the PCB shape/size/layer stack
Align components from the schematic physically on the PCB
Route traces
Additional holes, design features, assembly constraints, adjustments, silkscreen information, etc.