The common electronic components are resistors, capacitors, diodes etc. Other common ones are transistors and FETs.
When you buy a resistor, consider the most important parameters such as resistance value, tolerance, and wattage rating. But for buying capacitors, determine if they are polarized. The polarized capacitors can only operate where one side is a higher voltage than the other side. Besides this, you should determine the capacitance value and voltage rating. If you use inductors in the circuit, the tolerance and wattage considerations are much the same as with resistors. Then we discuss the diodes. Know for their voltage seen, current carried, voltage drop and Peak Inverse Voltage (PIV) rating because PIV is the limit of voltage the diode can be take when reverse biased without breaking down.
For transistors and FETs consider switching speed, voltage and current rating, power rating and so on.