This is just diplomacy on my part.
Q: What should one get with a mini lathe?
A: A bigger lathe.
I agree but until I build the shop building I have to start with a mini lathe.
Plus I think a mini lathe is a good place to learn some basics. And it seems that all of the "fixes", hacks, upgrades, and such for the mini lathe seem like a good way to learn some skills.
Get the lathe first, determine what will fit the lathe, then:
3 jaw chuck, if it doesn't come with one
4 jaw chuck, if you can only have one chuck, it should be a 4 jaw.
Dial indicator with a magnetic base, Noga is good
Quick change tool post and half a dozen tool holders
Chip brushes
Way oil
Spindle oil
A good light for over top of the lathe
Sturdy bench to mount the lathe to
Some high speed tool steel cutting bit
High speed tool steel parting blade
And the list goes on....
You're right, the principles and operations are the same. And if you fall into turning fountain pens (I'm serious, it's a big sub-group) you'll be set. As for me, I'm dying to move up to a 14-16" lathe, mostly because I don't have room for a bed over 40".
Get the lathe first, determine what will fit the lathe, then:
3 jaw chuck, if it doesn't come with one
4 jaw chuck, if you can only have one chuck, it should be a 4 jaw.
Dial indicator with a magnetic base, Noga is good
Quick change tool post and half a dozen tool holders
Chip brushes <---------------------------------------------------- IMPORTANT, also good for applying lube
Way oil
Spindle oil
A good light for over top of the lathe
Sturdy bench to mount the lathe to
Some high speed tool steel cutting bit
High speed tool steel parting blade
And the list goes on....
Don't forget about a couple files and some Emory paper