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/

Does EasyEDA not allow you to download gerber files anymore? Gerbers are universal and you'd be able to send them to any fab you wanted. Obviously EasyEDA being sponsored by JLC means they make it easy to order through JLC.