Modding an Optiplex 390 SFF
As big of an SSD as you can reasonably buy will work in that system. We can pretty much assume you won't be buying anything over 1TB.
I would not mess with the heatsink since it's designed with the hood to route hot area outside the case and not have it sit inside the small cramped case.
Check on the TFX size power supplies see if they match the size of yours.