The relationship between \$\beta\$ and \$I_C\$, \$V_{CE}\$
What general trends and rules of thumb are used to make sense of the varying β value? What are the factors and considerations for the varying β when you are designing transistor circuits?


The answer to the first question. You can use either negative feedback, or you can force a certain parameter set, and allow for variation. An example of negative feedback is using emitter degeneration resistors in Common Emitter amplifiers. An example of forcing parameters is using a current source to bias the transistor and then simply ensuring that there's enough current and voltage on the input to keep it linear. (which isn't hard for most signal level transistors)

As for factors and considerations for varying β, I've never personally bothered to take any other than "use the worse case β." If the β, is higher, then you get less current draw from the source: Win. If it's the worst, then no harm no foul. Also, taking the time to calculate Rin and Rpi never hurt either.

Finally, at the end of the day, if β is really important, Mosfets and Jfets have an almost infinite β (~10^9 -> ~10^12). See if that's more what fits your needs. After all, it's not like we've found some transistor that is all encompassing and perfect in every scenario.