You should never rely on someone else to keep your BTC secure. If you don't mind sending them your dox and answering personal questions, it should be OK for buying/selling BTC. I wouldn't recommend them for day-trading unless you only do so with small amounts that you wouldn't mind losing in the unlikely but possible scenario of Bitstamp ending up like Gox, and I would first make some inquires to check whether they have fixed their trading engine.