user16826: I'm rather new to filmography, and I just discovered that decreasing shutter speed can minimalist motion blur, which I want none of. I set my SS to 1/10000, but that obviously darkens everything. To compensate for that, I just increased the ISO until it looked normally lit again. It works, but something in the back of my mind tells me there has to be a downside to this. 
My camera is a Sony A7S, but I don't think that really matters

user17731: TL;DR: For most cameras, high ISO leads to a lot of graininess, but the A7S significantly less so than most others. However, try shooting test footage at different ISOs and see which ISO you like the most, or how far you can push the camera without the resulting image being too grainy for your liking.
Longer Answer: There is always a trade-off. With ISO, the higher you go, the more noise you get. On most digital video/movie cameras (think Red, Arri, Blackmagic, Aja, etc) a "high ISO," where you will get a lot of noise is pretty low, sometimes as low as ISO 6400. 
This is not the case for the Sony A7S (camera model does matter!). Take a look at this PetaPixel article. It describes (and demonstrates with examples)  the incredible low light/high ISO performance of the A7S (no, that's not opinion - the example images demonstrate up to 3 stops better performance compared to other high end imaging systems).
You'll want to carefully review some test footage to see how grainy is acceptable for you, and find that ISO sweet spot, depending on the look you want to achieve.

user14504: With an A7S, MkI or MkII; the camera is ridiculously incredible in terms of noise hint even at extreme ISOs; that's compared to just a few years ago when everyone was shooting on the 5D MkII. 
My recommendation BECAUSE it's the A7s and because the visually acceptable level of noise to the viewer is really not noticed until you go into the extreme ISOs; would be to try to maintain a consistent ISO regardless of whether you are indoors or outdoors, or at least a fairly consistent range. 
Shooting at 6400 ISO will have virtually no noise, and if you shoot all your material at a set ISO you will have a consistent grain/noise hint to all your footage. Just keep in mind you gain one stop of light each time you double your ISO. 
Shutter speed can be adjusted, along with your aperture; to set exposure; along with ND Filters if you have them. 
You should really shoot some tests at various shutter speeds to find the look you are happy with. The standard for film/video is a 180 degree shutter; which provides a slight amount of motion blur when shooting at 24-30fps (48-60 Shutter). When you have a higher shutter; your footage will be more "juddered", that is, each frame will have a higher sharpness value with each step up in shutter speed. This can sometimes be a little distracting. 
A great example of this is the D-Day Invasion Scene from Saving Private Ryan; shot at high shutter speeds; there is virtually zero motion blur frame to frame; and it adds to the scene's frenetic; racing feel. 

16826: <p>I'm rather new to filmography, and I just discovered that decreasing shutter speed can minimalist motion blur, which I want none of. I set my SS to 1/10000, but that obviously darkens everything. To compensate for that, I just increased the ISO until it looked normally lit again. It works, but something in the back of my mind tells me there has to be a downside to this. </p>

<p>My camera is a Sony A7S, but I don't think that really matters</p>
 17731: <p><strong>TL;DR:</strong> For most cameras, high ISO leads to a lot of graininess, but the A7S significantly less so than most others. However, try shooting test footage at different ISOs and see which ISO you like the most, or how far you can push the camera without the resulting image being too grainy for your liking.</p>

<p><strong>Longer Answer:</strong> There is always a trade-off. With ISO, the higher you go, the more noise you get. On most digital video/movie cameras (think Red, Arri, Blackmagic, Aja, etc) a "high ISO," where you will get a lot of noise is pretty low, sometimes as low as ISO 6400. </p>

<p>This is not the case for the Sony A7S (camera model does matter!). Take a look at <a href="https://petapixel.com/2015/07/04/this-is-how-good-the-sony-a7s-is-with-low-light-and-high-iso/" rel="nofollow noreferrer">this PetaPixel article</a>. It describes (and demonstrates with examples)  the incredible low light/high ISO performance of the A7S (no, that's not opinion - the example images demonstrate up to 3 stops better performance compared to other high end imaging systems).</p>

<p>You'll want to carefully review some test footage to see how grainy is acceptable for you, and find that ISO sweet spot, depending on the look you want to achieve.</p>
 14504: <p>With an A7S, MkI or MkII; the camera is ridiculously incredible in terms of noise hint even at extreme ISOs; that's compared to just a few years ago when everyone was shooting on the 5D MkII. </p>

<p>My recommendation BECAUSE it's the A7s and because the visually acceptable level of noise to the viewer is really not noticed until you go into the extreme ISOs; would be to try to maintain a consistent ISO regardless of whether you are indoors or outdoors, or at least a fairly consistent range. </p>

<p>Shooting at 6400 ISO will have virtually no noise, and if you shoot all your material at a set ISO you will have a consistent grain/noise hint to all your footage. Just keep in mind you gain one stop of light each time you double your ISO. </p>

<p>Shutter speed can be adjusted, along with your aperture; to set exposure; along with ND Filters if you have them. </p>

<p>You should really shoot some tests at various shutter speeds to find the look you are happy with. The standard for film/video is a 180 degree shutter; which provides a slight amount of motion blur when shooting at 24-30fps (48-60 Shutter). When you have a higher shutter; your footage will be more "juddered", that is, each frame will have a higher sharpness value with each step up in shutter speed. This can sometimes be a little distracting. </p>

<p>A great example of this is the D-Day Invasion Scene from Saving Private Ryan; shot at high shutter speeds; there is virtually zero motion blur frame to frame; and it adds to the scene's frenetic; racing feel. </p>
