Telescope selection for concrete uses Suppose I want to build or buy a telescope for the following uses:


Astrophotography (mainly galaxies and nebulae).
Transits of exoplanets and binary systems like Cygnus X-1.
To search for BH+star systems.
To measure the rotation curve of some spiral galaxies


Is that ALL feasible and/or cheap at amateur/semi-amateur level?
(1) is very doable. The others don't seem doable, at least not easily. If you practice astrophotography for a while you'll have a better understanding of the difficulties involved.

It's best (but not mandatory) if you begin doing plain visual astronomy, with something like an 8" dobsonian, for a year or two, to get yourself familiarized with how it all works. Once that's accomplished, the transition to astrophotography should be easier.

For AP (astrophotography) you'll need: a mount, a camera, a telescope. The mount is by far the most important. The camera is very important. Oddly enough, the telescope is the least important.

The accuracy, overall quality, and load carrying capacity of the mount will determine how well the whole system works. Just get the best mount you can afford.

Entry level mount examples: Celestron CGEM, Sky-Watcher EQ6.

Midrange mounts: Losmandy

High-end mounts: Software Bisque Paramount, Astro-Physics GTO



Cameras: for solar system objects like planets or the Moon, you'll need cameras with smaller sensors that can take lots of frames quickly (planetary cameras). For galaxies and nebulae (DSO - deep space objects) you'll need cameras that perform well with long exposure (DSO cameras); the best DSO cameras have cooler elements installed on the sensor.

There are OSC (one-shot color) cameras that don't require filters. There are monochrome cameras that require a filter box with R, G, B filters; you need to take separate exposures through each filter. OSC cameras are easier to use; monochrome cameras tend to provide higher performance.

Planetary camera examples: ZWO ASI 224 MC, ZWO ASI 178 MM

DSO camera examples: ZWO ASI 1600 MM, ZWO ASI 071 MC-Cool



Telescope:

For DSO it is very highly recommended to start with a relatively small refractor with short focal length. Something like the Orion ED80. Add a focal reducer / field flattener too. The long exposures require very high precision tracking from the mount, and a long focal length only creates problems. Keep it short until you learn how to make everything work. You could use a larger instrument like an SCT, but make sure your mount can carry that weight, and make sure you've fine tuned the process so the very long focal length of the SCT doesn't amplify the tracking errors.

For planetary imaging, the bigger the aperture the better. Use an SCT such as a Celestron C8 or bigger (up to C14 if the mount can carry it).



Capture software:

For DSO: Nebulosity (beginner), Sequence Generator Pro (advanced)

For planetary: FireCapture



Image processing software:

For DSO: Deep Sky Stacker (beginner), PixInsight (advanced)

For planetary: AutoStakkert for stacking. Subsequent processing could be done with Registax, or Astra Image.



Guiding:

For DSO, you'll do very long exposures. The mount alone is not precise enough. You need to guide it. This is done by using a smaller telescope (guidescope) installed on the main telescope, using a small camera (guide camera).

The finderscope that's normally used for visual astronomy could be used as a guidescope.

If you have a DSO camera and a planetary camera, you could use the planetary camera as a guide camera for DSO photography.

You'll have to connect the camera to a software that can control the mount and issue corrections to it. The most popular app is PHD2 a.k.a. Open PHD.

When doing DSO imaging, you'll spend most time during your first year basically learning all the subtle aspects of guided exposures.



Learning:

'The Deep-sky Imaging Primer' by Charles Bracken. A bit old but still very relevant.