It might be that I'm misunderstanding the definition of voltage. As it says "voltage is the work needed per unit of charge to move a test charge between two points."
I haven't checked their hypothesis, but it would appear to me that this implies that if you divide a joule (work) by a coulomb (unit of charge) you get a volt, which is a useful little factoid.
My confusion centers around the idea of 'per unit of charge', which suggests to me that amps and volts can vary independently (that is one 'unit' of charge may require different quantities of work to move between two points not related to resistance).
The per unit of charge just defines the relationship between the voltage(pressure) and the amount of material(units of charge) being moved in a test.
If that's the case, how can I = V/R be a thing? That suggests that current is precisely and deterministically derivable from voltage and does not vary independently.
Ohm's Law describes the interaction between voltage, resistance and current. You may think of voltage as being pressure, current the rate of flow, and resistance a measurement of constriction to the flow. If you apply the same pressure to a large pipe and a small pipe, more fluid will flow through the large pipe. The same applies to a large wire (low resistance) and a small wire (high resistance). This is resistance. If you apply a voltage to a large and a small resistance, more current will flow through the small resistance than the large one, though it will flow through both. If you know any two of the three values, Ohm's law will allow you to calculate the other. When you learn about RLC circuits and AC power, things become a bit more complicated, but when simply choosing and matching devices or finding replacements, Ohm's law comes in handy a lot.
Resistance of pure resistors varies by material, temperature, cross sectional size, and in the case of AC skin effect, by even more complicated geometry than size.
Silver is the best elemental conductor but some people think it's too expensive for power transmission, so a lot of copper and aluminum get used instead. Many other conductors are used for different applications (temperature, corrosion resistance, etc) and the resistance of each material affects its viability for each application. Copper is most commonly used in housing to minimise maintenance, but aluminum sees some use there and proceedingly more as conductor size increases, due to lower weight and cost. Many metals and conductive plastics are used as resistors for anything from the tiny circuits on small electronics to the large heating elements on a traditional electric stove. Gold sees use in platings (often extremely thin) for corrosion resistance and I believe also sees use for microscopic wires due to its ductility.
As a general rule, for reasonable DC voltages, if you double the cross sectional area of a wire, you halve the resistance and double current flow as a result.
Corrections by @G36, @Solar Mike =)