I don't pay for streaming media either but there is so much free on youtube and other places online that if I just want background noise I will never run out. (And we have a PBS membership that gives us free streaming to a huge archive of PBS and BBC shows. And the local public library has a couple of free streaming services too.)

But any new TV will let you hook up to a cheap external DVD player really easy too, yeah, and DVDs are resurging as more people realize streaming does not guarantee they can watch their show, so I think you'll be fine.

---sorry, I will evangelize at a moment's notice that 'streaming' doesn't mean 'paid subscription service', I should stop. :D