To answer your questions:
All are compatible with your motherboard.
And, m.2 devices are also compatible.
https://www.gigabyte.com/au/Motherboard/H310M-S2H-20-rev-10/sp#sp
No issue there.
To compare performance go to anandtech bench and pick two candidates for comparison.
https://www.anandtech.com/bench/SSD21/3005
You may not find 256gb candidates.
But, do not put too much weight on synthetic performance benchmarks.
An a gross level, all ssd devices perform well in normal work.
Some 2-6x faster in sequential and 40x faster in random performance compared to a HDD.
You will be hard pressed to detect any diference among any ssd devices.
Here is an amusing video:
View: https://www.youtube.com/watch?v=4DKLA7w9eeA
What I can suggest is that you spend a bit more if you can for a samsung ssd.
Puget systems thinks highly of them:
View: https://www.youtube.com/watch?v=4DKLA7w9eeA
Most will have a 5 year warranty.
Most ssd vendors will have a clone utility to convert your hdd to their ssd.
Samsung does also in the ssd migration app.
It is a C drive mover, not a clone. So long as the ssd is large enough to hold the used contents of your hdd it will work.
App and instructions here:
Download various software related to your product, including Samsung Magician, designed for use with Samsung's memory products, and find related information.
www.samsung.com