You can create a texture with DXGI_FORMAT_R16_SINT, which is equivalent to the "short/int16_t" type in C++ when running on Windows (there's also R16_UINT which is equivalent to "unsigned short/uint16_t"). You can see which formats are available for various use cases by checking the DXGI documentation for the feature level that you're targeting. For instance, here's the list of format support for D3D_FEATURE_LEVEL_11_0. If you check that list, you'll see that 3D texture support for R16_SINT and R16_UINT are both required for FEATURE_LEVEL_11_0. However if you check the support for Sample with texture filtering (interpolation), you'll see that none of the SINT or UINT formats are supported. So you wouldn't be able to get hardware interpolation if you want to deal with raw integers. However if you're okay with having your integers be interpreted as a [0, 1] or [-1, 1] floating point number, then you can use the equivalent UNORM or SNORM formats. These have support for filtering, so you could use hardware interpolation. You can also use filtering with FLOAT formats if you need to go beyond [-1, 1] range.
Buffer resources are generally going to be optimized for linear access patterns. So if you you have 1024 consecutive threads that each load from the buffer using their thread ID (e.g. thread 0 loads element 0, thread 1 loads element 1, thread 32 loads element 32, etc.) then a buffer is a good choice. Textures are optimized for 2D locality. So if you have 64 threads that access an 8x8 block of texels from a texture, then a texture is a good choice since it will probably be swizzled to match that sort of access pattern. If you need filtering then textures are also a good choice, since in many cases a 2x2 bilinear sample is the same cost as a single point sample or Load(). 3D textures may be optimized for 3D locality, but it depends on the hardware. Some hardware may internally store the 3D texture as N 2D slices, in which case texels from adjacent Z slices won't be adjacent in memory.
As always, if you really want to know for sure which is faster you will need to profile it.