I usually start where I feel the biggest problem is occurring, either the suspension or the LSD.
If the car is rolling around in the bends then I will start by stiffening the spring rates a bit to match the chosen tyres (more grippy tyres, higher spring rates).
If the car feels ok in the corners but is struggling to transfer the power to the road then I will start with the LSD, making note of the stock settings I try to think of how I could best solve the current problems when using the custom unit.
Concentrate on and deduce the main problems first, then refine.
Once I have a car behaving roughly as I want it to I will drop the rear toe to 0.00 so that I'm getting more accurate feedback from the chassis and then I will start changing one setting at a time being sure to test after every change so I can work out what influence each setting is having and how I can use it to make the car faster. My aim is to isolate settings, if you change a few different settings at once you will never be able to find out which one is making your car better or worse.
I usually start with spring rates, then dampers and ARBs. Toe is the last stage for final refinement.
I will keep going back and forth trying various combinations of suspension setup and LSD tuning until I find the right one for the task at hand, its basically a process of elimination until you find the right balance.
Once the suspension and LSD are nearly there I will put a transmission tune on it that suits the power curve and track. Its always a good idea to re-check your LSD setting once the transmission is tuned, you might now be accessing more or less peak torque due to the gearing and this can have a noticeable effect on the LSD. It might need to be set a few clicks higher or lower on all settings to match the original balance.
I wouldn't really say I've got a fixed way of approaching a tune, I just try to use my experience to enhance traits and decrease flaws as they occur, each car reacts differently to the last but the all follow the same basic principles and physics and you learn something new every time.
The tracks I use depend on the car being tuned, if its a fast, powerful car then theres no point taking it to a tight twisty circuit and conversely if its a lightweight, handling focussed car then you'd be out of place on a fast circuit with long straights.
I find the original trio of Grand Valley, Deep Forest and Trial Mountain to be a great set of tracks for checking a car is well rounded and able to handle different condition and road surfaces. They have a good mix of corners and straights, smooth surfaces and bumpy, uneven tracks.