We use Samsung SSD's in our iMac's & Mini's - It has no problems!
As to the newer Mac Mini:
- If you have a HD only model there won't be any problems as you have the needed cable and you don't have a Fusion Drive which adds some issues.
- If you have a SSD only model you will need to get the dual drive kit as the SSD currently in place uses a different connection (M.2).
- If you have a Fusion Drive or are adding a second SSD you will have some issues as the OS will want to create a Fusion Drive which in this case you really don't want. The other issue here is you need to break the current fusion drive set if you plan to repurpose the HD as the system will get confused seeing it when you try to use it.
As to how to prep the drive. I would recommend you do it externally via a USB to SATA adapter if your current drive is working.
As to doing a fresh install or migrate your current stuff over: Either way works, it all depends what you have on your current drive. You do want to leave 1/4 to 1/3 of the drive free so if you are going with a smaller SSD than your current HD then you may want to trim down what you have on the HD.
You also may want to look at the Western Digital Black2 dual drive which is a unique device! It is really two independent drives a SSD (120 GB) and a HD (1 TB) sharing the SATA port.