Very much this ^^^^This.
Make sure your comfortable changing a rear wheel puncture and start off with decent tyres like Schwalbe Marathons, rather than anything lightweight. Your brommie is very unlikely to disintegrate just because its ridden on consecutive days. How often does it let you down at the moment? - very very rarely i'd imagine.
Practice removing and refitting the rear wheel in the comfort of your own home. It seems a bit awkward at first but soon becomes second nature. There's an excellent instructional video on the Brilliant Bikes YouTube channel. I'd go for the Marathon Plus tyres for their puncture resistance although they can be a bit challenging to remove and refit ( again, practice makes it easier ) I'm running the Continental Contact Urbans at the moment and am very impressed. They seem quite puncture resistance and I find the ride to be smoother, plus they are lighter and a doddle to fit.