You should aim to get at least 6 confirmations before 1 Aug 00:00 UTC.

The likelihood of something major actually happening has gone down due to BIP91, but it's still possible. BCC will definitely split, though I expect its value to be nearly zero, so maybe you don't care about that one.

As a side-effect of BIP91 which is separate from the Aug 1 stuff, long reorgs are possible. Therefore, it's a good idea to require 5x more confirmations than usual before trusting incoming transactions. This is especially a good idea for the next 48 hours, but it'd be maximally prudent to continue this for the next month or so.