I've done quite a bit of 3D modeling using medical imaging working with various MDs for exploratory research projects.

For contrast, you'll want a CT because MRI typically isn't great for bone features but that inherently has radiation exposure which I doubt you'll have an MD sign off on if you're perfectly healthy. I don't recommend this personally but...

Ignoring that, most all radiology/medical imaging, especially anything CT based, uses DICOM as a standard data format. Many applications can read this data (everything from Photoshop, Matlab/Octave to libraries for languages if you want to go that far) but I highly recommend using 3D Slicer for your data processing:
https://www.slicer.org/

It's a fantastic piece of software often used in medical research for computational analysis work. It will allow you to import the DICOM data, read the metadata correctly to adjust/apply transformations on the data, and position the image frames in space correctly. From those frame stacks, you'll be able to do all sorts of things from volumetric viewing (computing interframe voxels), applying pre-mapped imaging specific color maps to the data, 3D volumetric rendering (with stereo support), and slicing/clipping which will all be useful.

There are lots of tutorials and even videos online for extracting 3D surface meshes from the 3D image data using Slicer. Some automatic thresholding will be useful to speed the process but you'll find for ball-and-socket joints, you'll have tediously define these regions on the 2D images frame by frame. From my experience the spine is the absolute worst based on the way the 3D geometries interlock. Assuming you have a high enough spatial resolution CT or series of independent CT scans, you'll likely need to step through the entire spinal column frame-by0frame to produce quality surface meshes. This process took me a good 4-8 hours just to do 4 lumbar vertebrae on a patient manually (constantly checking 3D geometry references to see if what I was doing was correct).

Once you're done with all of that, you'll then need to export all of these individual surface meshes (I'm guessing you'll want them independently segmented to play with/assemble, plus it'll likely be needed for 3D printing), you may need to down-sample/simplify the surface meshes and smooth them for printing. This can be done with a number of 3D modeling tools like Blender but I recommend Meshlab personally. There are a lot of approaches for this, google is your friend.

STL (or other surface mesh formats, say OBJ) will of course lose the DICOM metadata and scaling may become an issue depending on how Slicer exports the data and any additional post-processing you may do, so keep that in mind before printing that scaling may not be 1:1.

I used a cheap online printing service for my vertebrae project and scaled one of the lower lumbar vertebrae to about 1/7th actual scale for printing and that cost me about $30. A full scale lumbar vertebrae from the same service cost nearly $200 (this was about 6 years ago, no clue what prices are now). There may be better options.

You may also need to keep in mind 3D printing limitations during the entire process. Some 3D printers have maximum bounding box sizes (those arms only move so far) so your model can only be so big which may require you to break it into smaller parts and connect back together (glue? IDK, I've never done this). You can also shop around for services that can 3D print larger structures (I'm sure there's plenty) or do it yourself with some hacked out DIY 3D printer.

Most of the projects I worked on did this type of work because physically modeling bone in the real world with correct materials is quite difficult due to a lot of factors (I only 3D printed a scaled down vertebrae from one project as a keepsake for the work I did). Bones, for example, have a lot of smaller internal microstructures you may need to account for which was a critical concern since we were attempting to model bone fractures on a specific patient's vertebrae for a proposed experimental procedure and new process from a neurosurgeon. If you're interested in that sort of modeling, I found voxel based physical modeling techniques that work better than the finite element method/finite element analysis the group mechanical engineers suggested (he was comfortable with FEA/FEM).

The mechanical engineers working with us initially wanted to get cadavers in their lab do various physical stress tests on bone, but that was ruled out early on since we pointed out structural properties of decaying bodies were likely not representative of living bone/cellular structures (besides the "hey, dead bodies/limbs in our lab" fact)--plus, hey, computational science and modeling is cool ;)