The application itself determines the required quality of filters in terms filter specs and processing throughput in terms sample rate $F_s$ samples per second.
High quality filters will have tight specs and that will require high orders for a given type of filter. Different types of filters, however, can meet similar specs at quite different orders.
A filter of a given order, in return, determines the processing power requirements under a given data sample rate $F_s$. For example an FIR filter of order $N$ will perform $N+1$ MACs (multiply accumulate) per output sample of processing, and if the sample rate is $F_s$ samples per second, this means that the filter will perform $(N+1) \times F_s$ MACs per second of operation.
Therefore under a given sample rate $F_s$ and (FIR) filter of order $N$ your processor should be capable of performing $(N+1) \times F_s$ MAC operations per second. Given a CPU/MPU with a clock frequency of $M$ Hz, and MAC efficiency of $L$ MACs per hertz, then your processor should provide $M \times L > (N+1) \times F_s$ , discluding any memory operations etc.
This is for a single filter of typical implementation. There are a variety of architectures to implement FIR / IIR filters based on single rate and multirate techniques which can affect the processing power requirements depending on the application.
Finally, as a figure of very rough merit, for simple audio applications at $44.1$ kHz, an FIR filter of order less than $20$ will have weak properties. Where as orders between $20$ and $90$ will have (increasingly) mild quality and orders larger than 128 can have good and high quality characthersitics, where high quality refers to more control on the filter frequency response's spectral shape...
Be warned that thousands of taps might be necessary to realize a sharp transition, narrow band, FIR filter.