On a remote node, usually you run a PUBLIC routing node.

On a mobile you run a PRIVATE (non-routing) node.

On both cases, you don't have to keep all your stash !

As I explained in this guide, use the 3 levels stash:

https://darth-coin.github.io/beginner/be-your-own-bank-en.html

I've explained more the differences between private and public nodes here:

https://darth-coin.github.io/nodes/private-ln-nodes-en.html

and here:

https://darth-coin.github.io/nodes/managing-lightning-node-liquidity-en.html