I think one thing that is important is deciding on goals for why you are saving. Have short term goals and long term goals.
We find it very hard to save when we haven't got a set reason for it.
For example or short term goals are a few holidays and renovations we plan for next year, medium term goal is saving a deposit for our next investment and a big one month overseas holidays in the coming 2-3 years. Not currently saving for long term goals.
We also keep all our money in our offset account but I use a budget app that I allocate different amounts for each "envelope" (eg. Rates, electricity, health, Holidays, renovations etc) from each pay and shows the total amount in savings, so I can see what he money that is sitting in our account is actually allocated for. If you can do this, it will be better so you can keep saving on your mortgage interest. As different saving bank accounts don't have as high an interest rate.
Our budget covers every single expense from spending money to bank fees.