You can move all the files from your user's home directory onto the external drive. Applications and some app data must remain on the internal drive. That means the data stored in the Library folder inside your user's home directory must also stay on the internal SSD.
In effect that means you can absolutely buy a 250GB Mini and use it with an external SSD that you keep plugged in all the time - I would do it that way myself if I wanted to save money. The downside is you really must make sure not to store any user data on the internal drive on purpose.
For a 250GB drive about 200GB will be usable, then 50-150GB will be used up by the apps and for best performance everything that remains should be left unused.
You can check this on your current Mini right now, click on your user folder in Finder and press CMD+i to get the total size. Then do the same on the (by default hidden) Library folder inside. Finally, check the size of the applications folder.
Library folder size + application folder size is the amount of space you cannot move to the external SSD. As long as that is 150GB or less, it will work.
User folder size minus the Library folder that is inside is what you can move to the external SSD.
Again, it's not an issue to do it this way, but you will have a couple of drawbacks. You can't use the Desktop anymore to store files, as that will always go to the internal SSD. You can't use any of the pre-defined storage paths, so whenever you save a file and the save dialogue pops up and suggests a default location, you'll have to browse to the external SSD.
Just don't let the internal SSD run anywhere close to full. MacOS and the apps go into undefined behaviour territory when that happens, for example e-mail sync has messed up my IMAP synced mailboxes before when I ran out of space. You need to leave at the very least 50GB unused. Some of it will be used by MacOS for temporary swap space sometimes, that can be anywhere from 2-20GB.