I didn't think to mention this but since you mentioned HBO, Showtime and Starz am I to assume you have cable TV? With our digital cable subscription through Mediacom we have Video on Demand where you can watch movies for a price. Ours are $3.99 and less which is about the same as iTunes. We haven't bothered to try it since the movie selection appears to be similar to iTunes.
2015 Advanced RV Ocean One Class B
Visited states in an RV
I've been using Netflix, Hulu and Time Warner On Demand. I sometimes watch through my iPad using the iMainGo XP speakers (which I got hooked up with through my day job). The speakers are also a case and a stand, so it's almost like a mini-home theater system.
I have also used Redbox and they have a pretty good selection. If you want to check out the iMainGo, it's available on Amazon: http://amzn.to/iMainGoXP.
Here is a photo where I connected my iPad to my RV LCD TV with the Apple Component Cables. Works the same with an iPhone. You can also use the Apple Composite AV Cables.
I connect my iPad 2 with the HDMI adapter at home, Only 720 p, but a great picture. The IPad can produce 1080 p, but the video player can't, hopefully an upgrade will fix that. It also allows you to charge the IPad from the adapter.
Redbox is everywhere nowadays but the way I figure it for Redbox to be cheaper it needs to be within 1-1-1/2 miles of my house for it to be cheaper, not counting time, because it costs at an optimum at least 50 cents per mile to drive a car for gas, maintenance, insurance and depreciation. There and back twice to pickup and return is 6 miles total or $3 plus the rental of $1.25 vs. many services from the comfort of my couch at $3.99. My closest Redbox is 2 miles away.