Unless you're looking for specific vintage deep cut replays, you don't usually have a choice for which service to subscribe to for a given show or movie. So to watch that show or movie, your only choice is usually to sub to the service that exclusive rights to it. However, as soon as you've consumed the content on the streaming service you subscribe to, I'd recommend canceling it. There's no penalty for canceling. You can resub at any time. Every now and then there is a price break for an annual subscription, but if you're able to consume all the content in a couple of months, then even a cheaper per-month rate afforded by an annual subscription isn't a good value.

Subscribe to one paid service at a time, watch all the new content you want, cancel, subscribe to the next service. In 6 to 12 months there will be new content on the service you just dropped. Subscribe to it at that time. This way you can always have new stuff to watch while only being subscribed to one paid service.