Yes, continue to get paper statements and keep your mail. You will need it again for the next one.
And keep saving. The next visa is even more expensive. Currently £1,875 each (has nearly doubled in the last two years). I would recommend budgeting for £2,500 each. Hopefully it won't rise that much and you'll have a bit left over!
If you want to do citizenship immediately after you receive ILR, it's currently just under £1,300 each. <sigh> Almost there!