Friendly initial warning
Nikon 1 V1 offers really brilliant balance between cost and performance, especially in 2015. But does that mean using V1 as video camera will be cheap?
Hidden costs
Getting the V1 body or the default set with basic lenses is just the beginning. You need to keep in mind that in order to achieve eye-and-ear pleasing results, you will need to purchase some additional gear.
Stabilization devices
In most cases, you should not try to shoot handheld. V1 does not have any form of in-body stabilization and only few lenses do actually provide the stabilization (vibration reduction). So, you will need to get at least...
+ Tripod, $90 - $150
Solid tripod is the base. It should be robust, with ability to adjust yaw, pitch and roll via configurable head to make it possible to frame the shot as needed.
Rigs, gimbal stabilizers and other cool tech is also recommended, but not always needed. But you should not omit those when thinking about possible future costs.
Nikon 1 lenses
You will probably want to get the following two lenses, as they are truly "flexible friends". The first one does combine fast aperture with small dimensions, and it is ideal for street video or for example interviews. The second one is flexible zoom for summer shooting, but don't expect much help in interiors or performance in worse lighting conditions thanks to its relatively slow speed.
+ 18.5mm f/1.8, $249
+ 30-110mm f/5.6, $300
Reduction for lenses
While the mentioned lenses are good, the Nikon 1 lens range is very limited - especially the offer of fast lenses is basically restricted to two models. That means for real world projects you need to get reduction for 3rd party lenses, even if just for the ability to focus manually via dedicated ring.
+ mechanical reduction for your preferred mount, $80-$100
or
+ FT-1 Nikon electronic reduction, $300
Lenses
You just bought camera with interchangeable lenses. You will not resist buying new glass. Depending on your level of GAS (gear acquisition syndrome), this can be again additional $125 - $1000 for each piece!
Neutral density filters
Neutral density filters reduce the amount of light coming to the chip. If you plan to shoot outside, you will need this to be able to maintain reasonable exposure time along with fast aperture for that "oh-so-beautiful" bokeh shots.
+ ND4 filter, $75-$150
+ ND8 filter, $75-$150
+ ND32 filter, $75-$150
Advice: Buy as big ND filter as you can, and compensate the difference to lens screw via reductions (+ $15-$30 each).
Audio gear
The in camera audio from V1 is surprisingly good, but certainly not enough for cases like interview outside, club concert and other applications. You will probably need external recorder, such as Zoom H2 or Zoom H4.
+ external sound recorder, $200 - $300
Power supply
You will not want to risk running out of batteries during your shoot, so getting at least one backup is good idea.
+ EN-EL15 battery, $50
Video editing software
You did not invest so much money to gear to edit your footage in Windows Movie Maker in the end. You will need to purchase a reliable video editing software. There are some affordable solutions, and then there are some "ultimate solutions", such as Adobe Premiere Pro.
+ software, $125 - $600
Storage
You just got yourself an excellent video camera, you will shoot a lot of video to get better and better, right? That means lots of HD footage to be stored somewhere.
+ 2TB video storage cache, $125
You also need at least two decent SD cards to store the video when shooting. Spare no expense and get ones which will not fail you in future. Sony and Samsung offer some serious Class 10 cards.
+ 2x SD card, 2x$50
Summary
Shooting video with V1 is very exciting, rewarding and entertaining experience! But please keep in mind once you decide to go this route, it can cost you $3000 extra during a year after purchase easily, if you start from a scratch.
That, of course, presumes you get all that gear immediately. You will. It is inevitable, but you may delay the process to multiple years, to reduce the impact on your wallet a bit.
You can do a lot just with tripod, 18.5mm lens and Zoom recorder, presuming you have already the software for editing and you will shoot indoors, mostly static scenes. With this, we are getting to more reasonable price range.
Just... don't say I didn't warn you ;)