Period for trading should not start until deposit tx gets the first confirmation.
If you think it’s necessary to wait for more confirmations, you can wait a little bit more. But I don’t think it’s necessary, specially for trades under 0.5BTC.
I don’t think you’ll get penalized if you stay responsive since minute 1 of the trade. Trades can be completed even after end of the trading period, as mediation always have to be triggered from one of the peers.