And by vectors I mean the look of games like :
Would I be best constructing objects using LineRenderers? Or is it a case I need to use low poly objects with a suitable shader?
Cheers
If they are extremely low poly, you might be able to get away with LineRenderers and a big headache from setting them up based on your 3D-models 
But if you can find/write a suitable shader, you’d probably save a lot of hassle and draw calls
Vectorosity would be my tool for this. : ) You can convert 3D models to vector lines and it renders them very fast with few drawcalls.
You can use this for UI rendering
SVG Importer | Vector Graphics Plugin for Unity
Unity 4.6.0 Compatible, fully cross-platform.
Easily drag and drop your SVG files directly in your scene. SVG importer fully mimics Unity native sprites so your team doesn’t have to learn anything new. Extremely fast and simple workflow for rapid level design. Resolution independent graphics ready for retina displays and full support of the new Unity UI system.
SVG importer automatically converts SVG files into highly optimised meshes and does fully supports both
linear and radial gradients.
Features
- UI rendering
- Opaque rendering
- Transparent rendering
- Manual level of detail
- Depth compression
- Custom pivot point
- Drag & Drop
- Recolor artwork
- Automatic Colliders
- Full demo project
SVG Importer fully Supports
- Simple shapes
- Complex shapes
- Holes
- Linear Gradients
- Radial Gradients
- Strokes