Your plan is better than most people. But honestly 50k won't be enough. You'll barely fund the training and then you will need to pay for a type rating (20k). Keep debt free at all times.
My modular training cost in the region of 50-55k, 22k for a TR. A lot of money, but I stayed debt free and now earn in the region of 3.5k a month and have only been an FO for a few months, and the money will only get better. The training pays for itself...if you stay debt free and manage to get a job!
I wouldn't go integrated at all, unless you're on a cadetship. Especially with an airline like BA or Monarch, it might be a better option to take out a loan , go integrated and accept the cadetship!