There is never an always-right way to do something in audio. Really distorted audio can be beautiful, for example. That being said here is an example of a useful and commonly used plugin order with explanations for each processing type.

High pass filter – on the proper sources this is great on analog hardware, many microphones have a HPF switch. this is helpful to further processing because on many sources some low frequencies are not a part of the actual source but rather noise and possibly unwanted distortion. A good way to get started with filters is to look up that instrument’s range of pitch and then remove everything that doesn’t fall in that range. Here is a list I use often: http://www.independentrecording.net/irn/resources/freqchart/main_display.htm

Noise reduction, pitch correction, etc – While not important before or after an in-the-box HPF editing tools like these work best before most processing is applied for a plethora of reasons. Audiosuite is a nice option here as one can fix things on a clip by clip basis and have more processing power later. When rendering clips I like start with a duplicated playlist in case I want to modify the rendering audio later.

Noise gate – much like the above, gating can be done with a plugin or with fades/automation/clip gain/other editing. You want it to fire cleanly and it will work better before compression which limits the dynamic range of a signal thereby lowering the accuracy of the gate. Equalization and filters can affect your gating both positively and negatively. I find sidechaining EQ into dynamics processors to be very useful.

subtractive eq – much like a high pass filter (and perhaps the same processor to do both) pulling unwated frequences out of the signal before using compression will prevent the compressor from acting on those signals. You could also use an eq pre-compression to accentuate the compression of frequencies.

compression and other peak reducing techniques – Once everything has been cleaned up you can use compression to bring a track forward in the mix or add mojo. it can be a good idea to use multiple compressors here e.g. a fast compressor to tame peaks and then a slower compressor to bring a vocal forward in the mix. some compressors allow you to mix a wet and dry signal for parallel compression. parallel compression can allow for keeping dynamics in a track while liberally applying compression. It is possible to mix and match between many compressors all doing slight adjustments if you are going for specific goals and know what you are doing. Distortion/Saturation/tape emulation is an often overlooked trick to tame peaks as well and can get that sound you’re looking for faster than compression sometimes. It’s very worth experimenting.

additive eq – now it is safe to add to frequencies without mucking with the compressor. NOTE: sometimes you want to muck with the compressor.

harmonic distortion/tape emulation – bringing all the previous elements of the signal chain together might benefit from distortion and/or tape emulation. many different flavors exist but much of what gives a finished mix the tape sound is an accumulation of subtle tape emulation on many tracks

use busses to send the finished signal of a channel to aux tracks for reverb and parallel compression. this way your track outputs the dry level and the send feeds a 100% wet reverb at unity. you can adjust how much reverb there is for your signal by turning the send level up and down. this way instead of having many different reverbs on individual tracks the ‘space’ can be better shared. you can put an eq before the reverb on the reverb aux track if you want, as well. a compression track can add a nice glue to a mix, even a small amount of signal from several of the instruments can glue tracks together.