Digital. And something not toooo expensive. What do you recommend to start off with?

Hmmm, well Id say any of the Canon Powershot G series

G1X, G16, G15 are all pretty great. You’re looking around $500 ish for those. Thats the down side to digital. Larger up front cost. Anything below those Id stick with iPhone. 

You can get some great cheap film cameras like the LC-A for around $200. Thats one of my favorite cameras. You can see the work I’ve down with it HERE. I haven’t shot it in a while because my Leica really filled that place in my camera set.