The deposit amount for each model depends on its current current input and output cost as well as its maximum output.
All of this means that for every message you send, you are sending a deposit that should cover the max output scenario. And once you get your whole answer back, you get the rest of your deposit back

For some cheap model, with low cost and small maximum output you may send a 10 sat deposit and receive an answer with a 9 sat refund (so you only spent 1 sat).

For an expensive model, like Claude, with a large maximum output, you may be requiered to send a 1800 sat deposit and receive an ai answer back with a 1729 sats refund token back.

I put some sats in but found out that the one I wanted to use (Claude) had a minimum of 1800 sats. Is that because it simply costs more? Or does it generally use more resources?

Ecash & LN Paid AI

If you are willing to deposit sats through a lightning invoice, you'll get ecash from cypherflows mint and be able tk use paid models.