Short answer: NFW. It will drive most reasonable filmmakers nuts.
When you have a director making their first, second or even third film, even if they have worked as an editor and/or producer before its nearly impossible to do all three jobs well.
The film suffers from the inattention.
I have yet to see a director who is a good enough producer to do both jobs well and thoroughly, those two jobs are so different in terms of the mind set. Unless that director is really experienced i.e. has many years of solid directing, as in multiple films and formats under his/her belt. Directing requires complete focus on story, character, narrative thread, metaphor, historical perspective, and eye for detail and nuanced communication within the frame. Producing requires objectivity, intestinal fortitude, logistical oversight, attention to detail as it pertains to contracts, money, communication and strategic alliance building. Very different perspectives to work from and I have yet to see a director who is also an ace producer on the same project. You can be good at both jobs, really good, but to do both jobs at the same time is courting burn out and like I said the film suffers and who wants that!
That being said Stephen Soderberg has shot some of his own films and it works, so out of all the combos, shooting & directing could work well. It will save you money in the short run and in some cases clarify your intentions, visual strategy and set the tone. When you have a budget for DP, they will have a sense of what image style you're looking for because of what you shot (hopefully). Again, I think a great DP can be one of the most wonderful collaborators for the director. Many new directors rely heavily on the DP, rightly so, in many cases one of the most experienced people on the shoot is the DP. Due to the nature of their job, DP's work much more often than directors & producers because of the short duration of the shoot, they will spend at the most, on average, eight weeks on a shoot. Directors and Producers remain on projects for much longer periods, they have to be there for the full cycle of production. Since DP's are engaged on any given project for a much shorter amount of time, they are available to work on more gigs,therefore they have lots more practical experience when it comes to solving/composing shots, and set operations in general.
Editing and directing is a typical low budget arrangement, but even then, I have yet to see a film that did not suffer somewhat from the lack of objectivity that comes from directors who edit. Editing is a subtractive art, an editor is more likely to ask "How can I say this in as few gestures as possible?" Whereas a newer director is more likely to say the same thing in three different ways just to make sure the audience gets it.
New directors, are more likely to lose objectivity, to loose their own narrative thread. If a director is also the editor, that lack of clarity will often show up in the final product. They fall in love with shots and scenes and try to shoe horn them into the film, instead of looking at the film as it really is.
I worked on a great film that had three different endings, not an uncommon thing. It was a problem in the rough cut and in subsequent versions, and it was nearly resolved in the final version. The film as a whole was gorgeous and despite a few awkward "end-like" moments, continues to receive much deserved acclaim because of the artistic/experimental patina, the compelling subject and director's passion, persistence and ambition.
And here's the rub, by the time a film gets into the final stages, the film is what it is, and the editor is better able to accept the material and work with what's there. Whereas, the newer director is still very much interested in what they wish was there, which is why there are often 11th hour re-shoots, re-recordings etc...that ends up going nowhere. Because at this stage, the newer director is very insecure, afraid they have failed. And as soon as fear comes into the picture, the directors original passion and vision is eroded and replaced with far too much noise. An experienced editor will help the director get back to their original vision and will help them see that what they have is more than enough, what they have works and what they need now is to step back and look at the footage with fresh eyes and to reconnect with the subject in order to get out of their own way long enough to tell a good story.
What I've seen work really well, is when the new director has a more senior editor shaping the film and mentoring the director. What I've also seen work well is a new director partnering up with a producer with slightly more experience working side by side and learning together as they go.
That combination often works just as well since we all learn better from our mistakes, a more senior producer will be perhaps too seasoned to let the director make mistakes and tend to make things too easy for the director and thus the director has an inaccurate view of the process and what is possible given the time, finances and material.