As a hobbyist, I have had a good experience using EasyEDA [0]. It's free to use, with the caveat that you are pretty locked in to their PCB ordering service from China. However, pricing is crazy good, like <$50 total for 5 PCB's (although there will be tariffs).
Regarding your mental model, it's more like a 2-step process. First, you draw the netlist, which is the electrical circuit diagram. It's this stage you ensure there are no short-circuits, etc. Then in the second stage, you drag-drop the components to the physical layout you want. The software then has an auto-router that references the netlist and automatically generates the first pass of PCB traces. You can tweak them if you wish. The EDA software also has a rules engine that checks for correct trace spacing, vias, etc.
For a "baby's first PCB", I bet you have more skills than you realize and I would encourage you to just give it a shot. Also, if you make a small mistake, you can manually "bodge" the board by cutting wrong traces with an exacto knife and/or soldering wires to the pads.
Everything else just comes from experience! If you're staying in the sub-kHz (audio) range, you probably won't need the crazy high-frequency tricks/trace capacitance/trace-length-matching concerns.
[0] https://easyeda.com/