what type of cordage should I get for learning knots on? I looked around the other day and found I have no rope or twine in the house
I used to. I think 11-yo boy happened to it 
anyway, I need to go buy some. where shall I start?
what would be the most utilitarian rope to have in the house?
what would be the best for learning knots?
Just about anything will work to learn with. I would recommend against going too small because it's harder to work with. What's too small? Depends on your hands. For me, smaller than para cord can be difficult to learn with. On materials, I would specifically avoid polypropylene since it's usually slick and hard to knot. My personal preference for teaching class is 5/8" diameter, nylon or nylon/polyester in a solid or diamond braid. I find it at both Lowe's and Home Depot on the bulk rolls. I've found it's a good balance of small enough to hold easily, but large enough to see the structure of the knot. It's soft enough that the knots grip well and you don't have to fight it into position. On length, I've found 3'-5' to be a good length for learning most of the basic knots.
For general use it will be hard to use one rope for all uses. I would suggest going with a selection of small, medium and large to cover most uses. For small (~1/16"), I'd say either nylon mason's twine or jute or sisal twine. They each have their pros and cons which I can go into if you want. For medium, I'd say probably paracord or braided nylon 3/16" or 1/4" diameter. If you're going to only buy one I'd suggest going for this medium range size. In large, I'd look at nylon in 1/2" or 5/8". If you expect to lift/pull go for the larger diameter even if a smaller diameter is strong enough. The larger diameter gives you a better grip and is less likely to hurt your hands.
OK, I admit I'm a bit of a knot/rope geek.

Maybe I should start putting some of this into another post specifically about ropes &/or knots?