Real Component Characteristics

So the resistor lumped model(figure 1) is of far less concern than the others.

Typically the ESL(Equivalent Series Inductance) matters when you place a resistor on a gate of a a transistor and you begin to see some oscillation as shown in the example circuit in Figure 1.a.

This can be due to the LC tank that is produced with the various capacitance's of the transistor itself(Transistor Capacitance's: Collector to Base, Collector to Emitter, and Emitter to Base) modeled in Figure 1.b. Note if you are burning out transistors this can be a good indication of an LC tank creating damaging oscillations by building up heat within your transistor as shown in Figure 1.c below.

Furthermore, this ESL which is commonly not documented in the datasheet for most resistors can lead to odd frequency responses as frequencies increase, but unless you are getting into the GHz ranges it is typically less of an issue.

So the lumped model of a capacitor(figure 2) is probably the most important out of the trio of basic electronics parts to understand.

R1 is showing a leakage resistance, effectively this just means that there is some large resistance from terminal to terminal on this part that over time will allow any built up charge to "leak" out.

R0 is the most common thing to learn about when talking about parasitic, this is the equivalent series resistance, and is almost always specified on the devices datasheets.

Most commonly it matters when used in power supplies. A useful way to think about this is illustrated in the simple circuit in Figure 3. The ESR effectively acts like a resistor(R1) in series with the capacitor(C1). You want to charge up this capacitor but you lose out on some of the potential charge as it is dissipated as heat in the resistor. So the greater the ESR of the capacitor on a SMPS(switch mode power supply) the greater your losses are and the larger the ripple can be as shown in figure 4.

Depending on what you do the lumped model of a coil/inductor may be used all the time or nearly none at all.

L1 & L0 in Figure 8 is the ideal inductance value.

R0 represents equivalent series resistance.

Cp is the parasitic capacitance(changes depending on the case, conductor spacing, etc) and generally plays a major part in the self resonance of the part.

R1 represents the core losses in the coil/inductor.

Now with all of this in hand you would not have a hard time doing whatever circuit analysis you needed. However, acquiring/estimating these values can be less trivial. Generally you purchase parts and therefore are at the mercy of the vendor/manufacturer to provide this information. Even the information you'd need to "estimate" these values. So if you are interested in what that math looks like check out this link. That paper provides the equations and context needed to make such calculations/determinations and spares me from having to create my own demonstrations here.