**Core Concept**
The investigation of choice for unilateral mild axial proptosis, particularly in the absence of redness or pain, involves assessing the orbital contents and the extraocular muscles, given the possibility of a space-occupying lesion or thyroid-related orbitopathy.

**Why the Correct Answer is Right**
The correct investigation is Orbital Imaging, specifically **MRI of the orbit**. This is because MRI provides detailed images of the soft tissues, including the extraocular muscles, optic nerve, and orbital fat, which are essential in diagnosing conditions such as thyroid-related orbitopathy, orbital tumors, or inflammation. MRI is superior to CT scans in visualizing these soft tissues and is the preferred imaging modality in this scenario.

**Why Each Wrong Option is Incorrect**
**Option A:** CT scan of the orbit is not the first choice because it is less sensitive than MRI in detecting soft tissue abnormalities.
**Option B:** Ultrasound of the orbit is not suitable for assessing the extraocular muscles and orbital fat in detail.
**Option C:** Orbital Biopsy is an invasive procedure and not the first line of investigation for proptosis, as imaging can often provide a diagnosis.

**Clinical Pearl / High-Yield Fact**
In cases of proptosis, it's essential to remember that **MRI of the orbit** is usually the investigation of choice, as it provides a detailed assessment of the orbital contents and can help differentiate between various causes of proptosis.

**Correct Answer:** C. Orbital Imaging, specifically MRI of the orbit.