I ended up finding a lot of information on the Psyche Orbiter around 30 minutes after posting this, and I think I'll just write an answer to my question using the information I've found instead of deleting it.
What are we going to study when we send a probe there? Source
Specifically, the science goals for the mission are:
- Understand a previously unexplored building block of planet formation: iron cores.
- Look inside terrestrial planets, including Earth, by directly examining the interior of a differentiated body, which otherwise could not be seen.
- Explore a new type of world, made of metal.
The science objectives are:
- Determine whether 16 Psyche is a core, or if it is unmelted material.
- Determine the relative ages of regions of 16 Psyche's surface.
- Determine whether small metal bodies incorporate the same light elements as are expected in the Earth's high-pressure core.
- Determine whether 16 Psyche was formed under conditions more oxidizing or more reducing than Earth's core.
- Characterize 16 Psyche's topography.
The science questions this mission will address are:
- Is 16 Psyche the stripped core of a differentiated planetesimal, or was it formed as an iron-rich body?
- What were the building blocks of planets?
- Did planetesimals that formed close to the Sun have very different bulk compositions?
- If 16 Psyche was stripped of its mantle, when and how did that occur?
- If 16 Psyche was once molten, did it solidify from the inside out, or the outside in?
- Did 16 Psyche produce a magnetic dynamo as it cooled?
- What are the major alloy elements that coexist in the iron metal of the core?
- What are the key characteristics of the geologic surface and global topography?
- Does 16 Psyche look radically different from known stony and icy bodies?
- How do craters on a metal body differ from those in rock or ice?
What are the scientific instruments on the probe? Source
Psyche will fly a payload of 30 kg (66 lb), consisting of four
The Multispectral Imager will provide high-resolution images using
filters to discriminate between metallic and silicate constituents.
The Gamma-ray and Neutron Spectrometer will analyze and map the
asteroid's elemental composition.
The Magnetometer will measure and map the remnant magnetic field of the asteroid.
The X-band Gravity
Science Investigation will use the X-band (microwave) radio
telecommunications system to measure the asteroid's gravity field and
deduce its interior structure.
The last part of my question is sort of answered by the above, but also may be aided by an additional answer to touch more on what we can learn here over other asteroids.