A couple of insightful replies already....
So, to enlarge on the bigger picture, so to speak:
Editing in Lr is very different to Ps.
Ps is a pixel editor and the order of editing is absolutely crucial to a good result.
In other words one can edit in one direction only. (Yes, smart objects and its layers alter this somewhat...)
Lr, on the other hand, is a parametric editor. Edits are not applied to an image at the pixel level until a derivative image (TIFF, JPEG, DNG, etc) is created from the original raw image along with the parametric editing data.
Furthermore, only the net result of all the edits is applied at the pixel level.
What this means is that the ORDER of edits applied by the photographer is irrelevant - in other words how one came to the final position of all the sliders is completely irrelevant...
As already stated by the OP, and others, no slider operates in complete isolation to any of the others. This is particularly true for the tonal sliders. (Although the tone curve alters tonality (obviously), it does not change the actual settings of the sliders. However, according to the principles already explained when a derivative image is created only the net effect - sliders versus tone curve - is applied to that derivative image at a pixel level.)
Although my statement concerning the order of edits in the previous paragraph still stands in its context there are better, and less better, approaches to editing raw images in a parametric image editor.
My strong recommendation is to edit from the inside out. This is roughly opposite to the accepted wisdom of editing in a pixel editor.
What this means is to start with the mid-zones, then move to the highlights and shadows, and then migrate to the whites and blacks. In conceptual terms anyway the final edit (for tones) is the clarity slider. In practical terms, however, small remedial adjustments may need to be made as the editing process proceeds.
It also needs to be understood that the algorithms behind the tonal sliders (and tone curve) are image adaptive. What this means is that any slider manipulations are not absolute from one image to another. In other words moving a slider x units to the left or right will not have exactly the same effect from one image to another.
Astute readers may assume that what I am advocating is just the "accepted wisdom" of top-down tonal editing so beloved of Lr commentators, but actually it is not.
Although, from a tonal perspective I suggest starting with the exposure slider to shift those areas of the image that should be in the mid-zones into the mid-zones, I also suggest completely ignoring the contrast slider. The reasons for this are pretty clear:
Firstly, the effects of the contrast slider are global. Every part of the image is affected;
Secondly, the effects are symmetrical. This may sound like a good thing but honestly the way one needs to treat the highlights and the shadows are rarely the same; and
Thirdly, while the contrast slider certainly increases mid-tone contrast it has the effect of reducing contrast in the highlight and shadow areas and it is a very blunt tool in this respect. However, getting tonality correct in the both the shadow and highlight areas of an image, and normally, one is looking to increase local contrast in these areas. Unfortunately, the global contrast slider has the opposite effect and its effects are difficult to overcome.
So, the solution is to ignore the contrast slider and instead use a combination of the highlights and whites slider, and then the shadows and blacks slider to adjust the highlights and shadows independently of the other.
How, does one use the highlights slider and the whites slider, and then the shadows and blacks sliders in combination? Often, one is wanting to increase contrast in the shadows and highlights, just in differing proportions. The way to do this is to reduce the highlights slider but increase the whites slider. This increases contrast in the highlights. In a landscape image with white puffy clouds that appear blown and without detail astonishing amounts of detail can be be extracted.
The principle for dealing with the shadows is exactly the same. Lift the shadows but reduce the blacks slider will increase shadow contrast and improve discernible shadow detail. The beauty of this approach is that the shadows and highlights can be adjusted independently of the other.
How far does one take these particular edits? Again, there are certain principles that need to be applied against the aesthetic needs of the image. A high-key image is edited very differently to a low-key image. A landscape image needs to edited edited differently to a portrait. And I could go on and on...
However, certain principles do shine through! Obviously, it not generally a good idea to push the whites slider so far as to blow the lightest tones. (Specular highlights may be an exception.) In a landscape image I will often push the whites to just shy of clipping. How far to go in other types of images will be dependent on whether any true whites are present or not.
Adjusting the blacks slider is dependent on several factors. Mostly, one does want at least some areas of the image to be true black, although some high-key images may not require this. The other consideration is that, interestingly enough, our perception of colour appears to be calibrated against black. Without a true black for reference it is difficult to perceive colours correctly. This is as true for the editors of images as it is for the final end-viewers of that image. (This is predicated on the fact that appropriate steps to correct white balance as well as magenta-green colour shifts have already been undertaken.)
How far to reduce the highlights and increase the shadows is also a matter of aesthetic taste. In landscape images I will often max out the possible slider manipulations. So, I will frequently increase the shadows and reduce to the highlights as much as possible before manipulating the whites and blacks. Other types of images may not require such extensive manipulation of either shadows or highlights.
So far, in conceptual terms, the overall tonality of the image has been corrected (via the exposure slider) and the highlights and shadows have been adjusted independently of the other. In general, the result of the above editing will have reduced mid-tone contrast substantially! However, there is a slider that is designed specifically with this issue in mind. And that slider is the clarity slider. Increasing the clarity restores the mid-tone contrast although its effect is on local contrast. Because it is an image-adaptive edit it seems to have more effect in areas of reduced contrast - the mid-zones in this case.
I will often make small adjustments to both the blacks and whites slider after applying a clarity slider edit. This is normal!
Although the tone curve is a very powerful way to adjust tonality, my suggestion is to master the above sliders before trying to edit images using the the tone curve. In addition, the tone curve is not designed as a substitute for the basic panel tonality sliders, but rather as another tool to be used in a complementary fashion after the Basic panel edits have been completed.
My suggestion is to get to know what each of the Basic panel sliders really do. The best way to do this is to max out the adjustment of each slider in turn to see what it is doing and then pull back the setting to a more reasonable setting according to aesthetic needs. Understand that some sliders are designed to be used in combination (whites/highlights and blacks/shadows). Also understand that Lightroom has been designed for beginners as well as experts. What this means is that 'auto tone' is for complete novices who have no idea, and the results using 'auto tone' vary from vaguely acceptable to downright horrible depending on the starting image. The contrast slider is also for beginners who need to adjust mid-tone contrast (with the consequent unpleasant side-effects for both highlight and shadow contrast).
In contrast (pardon the pun) my advice is aimed at those who aspire to becoming very accomplished image editors using Lightroom as their preferred parametric editor.
Once one becomes conversant with the abilities of the Basic panel sliders, and just as importantly, has a pretty good idea of what needs to be done with an image from an aesthetic and artistic perspective, then actually editing that image (from a tonal perspective, anyway) only takes seconds. Even if I need to round-trip a couple, or more times, around each of the sliders to fine-tune that image, it still only takes seconds! In fact it has taken a truck-load of time to type this reply, but a fraction of the time would have been sufficient to actually demonstrate all these principles in Lightroom - complete with explanations!
Tony Jay