Rob-F, I use a so-called pico projector sometimes, for my digital images. Pico projectors are cheap but dim and short-throw (less than 6 feet). They work great for projecting in a small room on a white wall, or better on a screen. I wouldn't call them the equivalent of a slide projector, but they are very convenient.
I am not sure how much a proper projector costs, but last time I looked they were very expensive. Also their resolution is based on video projection so not super great unless you go for high-end latest tech home cinema gear. Digital projectors also come with different signal processing and different lamp technology and are quickly superseded.
As you can tell, i am not a fan. I'd say the TV idea is better.