OK, this is way too long of an answer I know, but I couldn't help myself! So here goes:
First of all, welcome to APUG! I have to say that there are so many tradeoffs in camera design generally, and also so many specifics about exactly what you have in mind for this camera, that it is a little hard to give too firm an answer to many of your questions just yet. There is also a certain amount of understanding of the basic optics of lenses and imaging that you really ought to have before thinking about producing such a camera. But I do like the idea a lot, and admire you for considering doing it!
So let me see if I can at least point you in the right direction and maybe answer a few specific questions along the way:
For the one question, the distance between the lens and the film technically depends on where you want to focus! You can look up the
lens makers equation that was referenced earlier to see how the relationships are calculated, but a couple key points you should know:
- For things at infinity (or at least "far away") to be in focus, the distance between the lens and film should basically be equal to the focal length of the lens
- To focus on progressively closer subjects, the lens-to-film distance would need to be progressively increased. For example in the example you gave of a lens with focal length of 120mm, placed 200mm away from the film, you would be focusing on very near objects (300mm to be specific, or about 1 foot away from the lens).
- This brings up the bigger question of whether you even want the ability to adjust focus at all, and also the question of why box cameras like your Brownie Six-20 don't have adjustable focus lenses. The answer has to do with the concept of Depth of Field (or DOF). This is basically the idea that while you get optimum focus only at a certain distance from the camera, there is a range of distances for which the focus is "good enough" and for which subjects within that range will be acceptably sharp. There are equations for this too, and online DOF calculators you will find to play with. But the main thing you need to know is that shorter focal lengths and smaller diameter lenses (or smaller opening diameters) make for greater DOF, and thus offer the possibility of getting by without the need for a focus mechanism. By the way, the ratio of these two quantities - lens focal length and lens opening diameter - is the rough definition of f-number (or "f/#"), and larger f-numbers mean greater DOF.
- Your Brownie also uses the trick (one which I really like, by the way) of offering an auxiliary lens which can be swung into place specifically for focusing on closer subjects. It is something you could consider, depending on how inexpensively you can get lenses.
You should also consider the Field of View (FOV) you want the camera to have, i.e., how wide or narrow the angle of coverage captured onto the film. This quantity depends on both the lens focal length and the format of the film you are planning to use (i.e., the physical size of the image actually captured on film). So as you can see, it is a little hard to specify things like focal length without working out those factors first. But as a starting point for consideration, your Brownie has a focal length of 110mm, and an f-number of f/11. If you have some feel for the FOV that camera produces (and whether or not you like it), and if you can specify the size of the film frame you are wanting to use, we can help you work out some general specifications for things like lens focal length, lens-to-film distance, etc.
As one example of the basic tradeoffs that come into play when designing a camera, consider this: going with smaller lens openings and higher f-numbers will give you greater DOF and thus more of the picture in good focus; which in turn means maybe you don't need to have a focus mechanism. However smaller lens aperture means either longer exposure times (which means greater chance of blur due to movement of the camera during the exposure), or else having to use higher speed film, up to the limit of whatever is available.
There are a whole bunch of subtleties that arise when thinking about these things, like where to measure distances from on the lens, what shape of lens to use, where to place the aperture in the camera, and so forth. But it is not worth worrying about those details until some of the first order concepts are decided upon - things like the film size you will be designing to, the field of view you want, whether it should be fixed focus or variable, whether it should be "point and shoot" or have some degree of exposure adjustability, and just generally how simple or sophisticated you want to make it.
