Osiris settles in Bitcoin and Monero — the modern default pair for hidden-service commerce.
BTC XMR
Use Monero unless you have a specific reason to use Bitcoin (almost always: the vendor only accepts BTC). Privacy properties of XMR are protocol-level; Bitcoin’s transparent ledger is the trade-off you take by paying in BTC.
Deposit confirmation count
Bitcoin credits to your account balance after about two confirmations. Monero takes around ten blocks, which is roughly twenty minutes wall-clock. You'll see the pending balance update as confirmations roll in. There's nothing special about the Osiris flow versus other markets — standard Tor-market deposit workflow.
Why no Litecoin or Ethereum
Osiris hasn't enabled native Litecoin or Ethereum acceptance. The operator's focus is availability and the BTC/XMR pair is what most buyers and vendors actually settle in. If you specifically need LTC, see the markets that take Litecoin — Nexus, Anubis, Mars. If you need ETH, that's Anubis.