It's not all improv. The script is complete with dialogue, but I said my actors will have room for improv. Watch any movie Vince Vaughn is in, he improvises all over the place on top of the dialogue he's already memorized.
Also, when I say my actors will be free to move around the space, I'm not talking about a chase scene or something crazy, it's movement around in a bedroom, or inside a bookstore. It's really not that difficult to follow someone walking and adjust your focus as they move, especially if the style of the film doesn't require everything be in focus all the time. It's art, not science.
As for continuity, the style that I'm going for does not require tons of cuts. I'm going for long takes, and sometimes I'll even have 2 cameras running.
One recent example of a film similar to what I'm going for is "Like Crazy." That was shot on a 7D (although they had better lenses than I will) and was completely improvised. I think they had something like 40 hours of footage that the director just went through and cut into a concise film. Like crazy got into Sundance and was purchased by Paramount for $4 million.
It can be done.
From earlier posts, it sounds to me like you're making mumblecore. Cool! You'll catch no grief from me.
I wouldn't look to "Like Crazy" as your model for success, though. That is, unless you've got a couple big name actors/actresses in your pocket, and you're shooting your movie for half a million dollars. I think the most recent movie you should be looking to for a map to success is "Tiny Furniture".
There are a couple things I'd like to address, though, and they do apply to your original question.
First of all, in which genre does focus not matter? It's annoying when the subject goes out of focus. Your audience is doing a lot to suspend disbelief, and you're not helping them when you remind them that what they're watching is artificial. Losing focus takes people out of your movie.
For that reason, though I doubt you'll consider this, I almost think it might be wise to ditch DSLR and just get a really nice video camera, and let auto-focus do it's thing. Either that, or shoot for as wide a DOF as possible.
I'm basing that on your plan to ask the cast to improvise. I love improv. I love Vaughn, but I really doubt he's just going all loosey-goosey. Improv normally has a structure to it. If you want your movie to be visually interesting, I think you should at least have blocking well-rehearsed. Needless to say, this would greatly help you pull focus, especially since you seem to be fond of shallow DOF.
Anyway, all things considered, I agree strongly with jax_rox, in that I think you should get a zoom. With the nature of your shoot, versatility will really be your friend, and there's no reason why you need a prime for every damn shot.
Lastly, though this doesn't really apply to the question of focal lengths, dude, though the style of film your making fits well with lots of long takes, the manner in which you plan to make it does not. Improv is
incredibly difficult to edit, and long takes are going to be rare.