Regarding his general position, I would sum it up as:
He is okay with using the machine to avoid catastrophes, especially catastrophes caused by his time machine, but this is flexible
Just, to point out though:
This wasn't the purpose of the time machine
Doc states quite clearly in II that he invented the time machine to understand humanity i.e. he wants to see where humanity has been and where it is going. So, let's be quite clear that Doc didn't invent the time machine to manipulate the timeline; he only wanted to observe.
Back to the
Let's consider the major alterations to the timeline made in the trilogy:
- In I, he wants the timeline to be restored, which has to involve altering the timeline, but for the greater purpose of avoiding a paradox
- In II, he wants to alter the timeline, but that was because Biff had altered the timeline
- In III he doesn't want to alter the timeline, but is okay with doing so (only slightly) to save Marty and his own life
But, in my opinion, the two most important alterations of the timeline were the beginning of II when he comes back from the future to prevent Marty Jr from being caught which starts a chain reaction, and at the end of I where he wears a bullet proof vest, preventing his own death.
Regarding the first, this clearly involves changing the timeline, not for a greater good, but to help out Marty and his family. So, based on this, I believe that Doc's position on altering the timeline is something along the lines of the fact that he was okay with making alterations for a greater good.
Similarly, when he wears the bullet proof vest, it's for his own gain (okay, you could argue that it was for Marty's gain as well as it would be devastating for Marty to lose Doc, and our gain because if Doc had died we wouldn't have had BTTF II or III). His rationale behind this was 'What the Hell' - not exactly a hard and fast rule to apply.
On your last point about is he ever worried about these changes, he most certainly is! Near the beginning of III after Clara is saved and Marty tells Doc the story about the ravine, Doc is very worried about the potential implications of changing the timeline like that. At the end of I when he learns that Marty may have seriously altered the timeline by having George punch Biff Doc also expresses concerns, but doesn't go into this much due to the time constraints.
As for his concerns about the positive effects for the McFlys and the negative effects for the Tannens, as I mention above Doc is concerned about the former at least. He clearly shows some concern when he speaks to Marty for the last time in 1955 about George having punched Biff. Regarding the Tannens though, he doesn't show much concern generally. This is possibly because Doc doesn't have a great deal of interaction with Biff throughout the films.