Mecha Rail Launchpad Building techniques?
Based on your drawing and description, the closest analogy to your idea would be a railway turntable, where the mech bays would be akin to the roundhouse and the "exit" on your diagram represents the connecting railway to the turntable switching yard.

LEGO models of such structures can be found and analysed for their various building techniques to see which ideas would suit your expectations and situation.

Rails: yes or no? Obviously these models are designed with LEGO railway pieces in mind which might or might not be suitable for your MOC. Using the existing railway system offers a few advantages, like a complete ecosystem for straight and curved rails, wheels, carriages, switching points, couplings, etc. and might even look suitably industrial and heavy-duty. On the other hand their usage seriously limits the possible geometries (wheelbase length, minimal height of the carrier trolley, etc.), defines the look of the model and might provide challenges with the connection of the turntable and the static rails. Another option would be to use carrier trolleys with rubber wheels on a tiled surface to get around some of the above restrictions.

Implementation of the turntable itself The basic component is a circle-shaped, pit-like structure with a radius big enough to fit a carrier upon the rotating bridge above it and with enough depth to house the end supports, the central pivot column and the mechanism used to motorize it if needed. The central pivot and the end supports must be strong enough to hold the combined weight of a carrier and a mech on any point along the tracks on the turntable, which would mean either really sturdy supports or a carrier long enough to distribute its weight among multiple supports and the ground around the structure.

SIDE CUTAWAY VIEW OF THE PROPOSED STRUCTURE
                                        MAGNIFIED VIEW OF 
 mmmmmm      mmmmmmmmmmmmmmmmmm       THE DRIVING MECHANISM
 oo==oo      o==o   o==o   o==o    /   ----------  -------
 ------ ----------------- ------  /         d|b3   MMMMM##
 ######  T      A      T*~MM#### &lt;           *~~~~~MMMMM##
 ######  !      H      !  ######  \                MMMMM##
 ########^#############^########   \               #######

Legend:
# "Solid" ground
- Rail for the mecha carrier trolley
o Wheels of the carrier
= Structure of the carrier
m Feet of the mecha, or upper structure connecting multiple carriers
T End support structures
! Support structures with tiny wheels on their bottom parts
^ Suitable rolling surface for the end support wheels (rails or tiled surface)
A Central axis pillar
H Central pillar structure
M Motor for driving the ring
3 The inner gear rack of a Bucket Wheel Excavator ring
d|b A gear with a vertical axis, meshing with the gear rack ("3")
* A mechanism for turning a horizontally rotating axle into a vertically rotating one
  (like two bevel gears or a gear and a worm gear)
~ Horizontal axle


End supports and their wheels The end supports must travel along the bottom edge of the pit, supporting a great portion of the carrier and the mech, while losing not too much energy to friction. This calls for wheels, but even here we have many options:


You can certainly use generic railroad tracks if the dimensions permit it (the radius of the pit is just a few studs larger than the outer curve radius of the LEGO rail pieces)
For smaller dimensions the narrow gauge rail tracks might be used
The newer roller coaster pieces could be an alternative if a suitable wheel setup can be constructed either from scratch, or built around the existing rollercoaster cars
At least one example I have seen uses monorail tracks, if you have those, feel free to use them this way
Tiles and road wheels are certainly the most flexible option regarding the possible diameters but they tend to have a lot of resistance compared to non-flexible wheels on rails
Some Technic sets, like the 42054 Claas Xerion tractor, the 42082 Offroad Crane or the 42055 Bucket Wheel Excavator for example feature such turntable solutions that can be used as inspiration


Motorization You haven't mentioned if you'd like to use a motor to drive the turntable, but if yes, then you have a few options here as well:


Train engine on rails as the "feet" of the end support(s)
Motor housed in the end support(s) propelling against the wall of the pit
Motor housed in the central column
Motor housed in the wall of the pit propelling the turntable by its edge


The first two options require either a battery and control system built into the moving parts of the turntable itself, or wires that can feed the built-in motors from a static battery - but this option must be used with limiters or the wires might get tangled or snap. The third needs extensive gearing down to be able to handle the load and all losses without overstraining the motor. The last option avoids these problems but requires the turntable to be a complete ring with an interface suitable for propulsion (either a smooth circle that can be driven via friction from multiple rubber wheels, or a circular gear rack - The specialised parts from the Bucket Wheel Excavator or the 4481 Hailfire Droid wheels would be my first idea).

If you have any more questions, either in general or regarding a specific problem, feel free to ask - I'd love to see your project come to fruition :)