Black and white DSLR video quality
I can't help you with the set lighting but the look of the video is definitely achievable in post and in case of a modern camera you definitely have to do a lot in post to get a believable "retro" look. After Effects is recommendable due to many great plugins that help achieving specific looks but any editor that has good color tools on-board, a blur filter and a good grain filter will do the job to get the desired effect.

Punch the highlights, deepen the blacks, you generally want high contrast but don't just use a contrast effect in your editor, that won't get you very far. Level Curves are always a nice utility for these kind of things. Play around a bit.
Add a very slight blur, 0.5-2 pixel blur should be enough. Try different blurring algorithms if more than one is available to you.

The shots are also out of focus a little in almost all scenes. If you can re-create that during the shoot you could possible spare the blur in post all-together and get an even more convincing look.

Use a tool like Filmconvert to add a subtle grain to the video. You can also use onboard tools in your editor though most plugins offer a more realistic film grain than the average simple noise generator.

Filmconvert offers also to match the colors to the colors of a certain "old" film camera, which might help you. An example of a B&amp;W movie that used the plugin: http://www.filmconvert.com/Videos/Video.aspx?id=224&amp;order_by=staff_picks&amp;page=6

Keep in mind to not over do it, the border is thin between unrealistic and believable "retro look".

If After Effects is available to you I can recommend the RedGiant Color Suite (many of these products also work in Premiere and other tools). Though you can also use Premiere with Speedgrade (which nicely integrates into Premiere now) which will bring you similar results with similar ease of use as with After Effects if After Effects isn't your thing. Though After Effects offers a huge amount of editing capabilities which help greatly creating very specific effects.