Whenever you design a system, it helps to break it down into smaller, more or less independent chunks. That way you can focus on one chunk at a time, then focus on connecting the chunks to each other.
Almost every system starts from the same basic block diagram:
where the boxes represent circuits and the arrows represent wires between the circuits (if you want to get fancy, you can call the arrows 'signal protocols' and list the rules for what signals will travel through the wires).
The diagram is recursive, meaning you can replace any box with another copy of the same diagram. An LCD backpack is a moderately complicated circuit, but as far as your Arduino is concerned, it's just 'output'. The basic rules are "anything outside a box can safely ignore anything that happens inside the box" and "anything that goes into or out of a box has to travel along an arrow."
There's no single way to break a system into boxes, and you only need enough boxes to help you think about the system without getting confused.
The nice part is that the diagram gives you some basic hardware design for free. Each box can be its own PCB, and each arrow can be its own set of cables. If you want to combine multiple boxes on the same PCB, you can still treat the circuits as separate units.
Once you have a system diagram that works for you, start listing conditions each box has to satisfy beyond the basic 'makes the system work' stuff.. "this input has to go by the front door", "this input has to go by the back door", "this part needs to stay plugged into the wall", "that part needs to be portable", etc. Once you have the system requirements and physical requirements, you'll have a much better idea of how to build each box.. which ones can live on the same PCB, which ones can live in the same enclosure, etc.
When it comes to building the actual circuits, there's a whole laundry list of methods: freeform, point-to-point, cordwood, dead-bug, Manhattan, wire-wrap, protoboard, pad-per-hole board, stripboard/Veroboard, Perma-Proto, or full-scale PCB. They all have their pros and cons, and interestingly enough 'full-scale PCB' isn't always the best choice.
When you void a product warranty, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.