If you can afford it, a smart trainer and Zwift are definitely worth it. If not, it's not the be all and end all and there's many more ways to go about it. Just get yourself some sort of training plan and be consistent with it. Just a standard mag or fluid trainer (they go pretty cheap in this modern smart trainer era) combined with some workouts on Youtube and you will be smashing next summer.
Also look at getting at least some slicker and higher pressure tyres for your ride. If the road is where you'll be spending your time, it's well worth it