You can do a backup within J River (File - Library - Back Up Library). That will create a zip file that you can move to the new computer. Then do a library restore and you library will be moved. You have to have the same path name to your files on the external hard drive. It is best to use a mapped network drive (like Z:) for your files since you can remap the definition as needed when you move files. But as long as the path names are the same you should be OK.
To see where the art work is stored look in Tools - Options - File Location. If you have Also store in file's tag set your cover art should be fine, if you are using a format that allows cover art as a tag (like flac). You can look at the tag of any given track and check Image File to see where the cover art is stored for that track.
If you want to make changes across the whole database for the path names you can use Tools - Library Tools - Find and Replace. You can use that to change the path name to a mapped drive (like z:) to make moves easier in the future. I would be sure to make a library backup before trying Find and Replace - just in case. It is probably best to do it on the new system after the initial restore.
To see where the art work is stored look in Tools - Options - File Location. If you have Also store in file's tag set your cover art should be fine, if you are using a format that allows cover art as a tag (like flac). You can look at the tag of any given track and check Image File to see where the cover art is stored for that track.
If you want to make changes across the whole database for the path names you can use Tools - Library Tools - Find and Replace. You can use that to change the path name to a mapped drive (like z:) to make moves easier in the future. I would be sure to make a library backup before trying Find and Replace - just in case. It is probably best to do it on the new system after the initial restore.