Electronic – Drive FET/transistor based on 2 different resistances

If you wish to avoid holy wars you'll need to avoid making simplistic and incomplete statements :-).

Bipolar transistors are current driven.

MOSFETs are voltage driven.

In both cases the spread of parameters during manufacturing is such that a circuit will almost always rely on feedback to produce a given voltage or current gain.

MOSFETs tend to be slightly more costly at the very bottom end for "jelly bean" applications. But, for switching more than a few ~100mA, MOSFETs are usually as cheap or cheaper than functionally equivalent transistors, are easier to drive from a uC (microcontroller) as a digital switch than bipolar transistors and tend to have very significantly superior on characteristics.

An "on" bipolar transistor exhibits a saturation voltage. This can be several tenths of a volt and to get it much under 0.1V usually requires a high base to collector current ratio that is undesirably high. At 1 A a 0.1 \$V_{sat}\$ (saturation voltage) dissipates 0.1 W and is the equivalent of a R = V/I = 0.1/1 = 100 \$m\Omega\$ transistor. But at 10A the figures are 1 Watt dissipation and 10 \$m\Omega\$. The 0.1V is very difficult to achieve at higher current levels.

The \$R_{DSon}\$ (Drain-Source on resistance) of MOSFETs is typically under 0.1 \$\Omega\$ and you can get devices with 10 \$m\Omega\$ or even sub 1 \$m\Omega\$.

As switching speeds rise MOSFETs need a gate driver to charge and discharge the gate capacitance. These can be relatively cheap.

More soon ....

The arduino interface won't work as-is, but the rest looks good.

When the switch is on, the arduino's transistor will probably not like the emitter and collector both connected to +24v while the base is at +5v or whatever the arduino gives you. That's -19v, which is probably outside of the spec.

When the switch is off, the arduino will only be able to supply about +4.3v to the load (5v - Vbe) because the transistor is then operating as an emitter-follower.

The concept should work, but you'll need a slightly more complex interface from the arduino. Probably use either a PNP or a P-channel FET across the switch with a pullup resistor to +24v, then pull that down with either an NPN or an N-channel FET that is driven by the arduino.

As for your other questions, go to mouser.com or digikey.com or any other electronics warehouse and plug your requirements into their parametric search engine, one parameter at a time, most important first, and select as many options within each parameter as will technically work for you. When you run out of requirements, sort by price at your required quantity or round up to the next common price break.

Sometimes, the specs that you care about are not listed in the parametric search. In that case, specify what's there, sort by price, and start reading datasheets. For example, the base resistor for your ground connection depends on the maximum base current and the transistor's gain. You want enough base current to saturate the transistor (make more current available to the load than it will use), but don't exceed the maximum.