It has been mentioned a few times that BA CitiExpress et al prefer recruiting low hour pilots who have an integrated course although bear in mind that we are currently in a tight market. By the time you qualify the situation may well (hopefully) be very different and a modular/ integrated course might not make any difference. Even though money seems to be no object now, flight training always takes longer and costs more than you bargined for so it may be wise to hang on to as much spare rhino as possible. You may need it to keep current / pay the bills once you are qualified. Is there really any need to spend more than necessary?
Either way though get started asap. You won't regret it.