Is Raiden network only suited for ERC20 token transfers? Does / will it support other token standards (e.g., ERC223) or simple ETH payments?
Yes, currently only ERC20 tokens. For one thing, it uses the
transferFrom() mechanism that ERC20 provides, but ERC223 doesn't.
However, other non-ERC20 tokens and Ether itself can fairly simply be wrapped into ERC20-compliant tokens using smart contracts (E.g. you send the contract some Ether; you get back some ERC20 tokens that you can convert back to Ether at any time via the same contract at a 1:1 rate). So this limitation is not as severe as it may seem initially. This process could even be automated by the Raiden client or netting contract.