Well the bale of straw/hay bit is an unusual, some would say "fad", approach. Works but not for the inexperienced. Any quality potting soil-less mix is the norm for use in any container and the most 'guaranteed' if you will approach. You can add some compost to it if you wish - optional - can't hurt, might help.

Dave

Last year when I did container potatoes, I grabbed the cheapest bulk potting soil at the hardware store. Then I mixed in a little dried manure and compost, for good measure. They did great. The volume of potatoes seemed to depend much more on the breed of potato than anything else.

This is a plant that grows well in Idaho and Nevada, which are high plains deserts that support sagebrush very well. The more nutrients they get, the more potatoes you'll get... but they're very good at growing in less-than-desirable conditions.

I typically fill my containers about 80% full with regular potting soil and mix in some PRE-MOISTENED peat moss to give the potatoes the acidity they need. It also helps to prevent potato scab. I've had good results so far!
Kim

Here is a link that might be useful: My Garden and Potatoes

Hi Kim. I am brand new at gardening and I am going to grow potatoes in smart pots. I am wondering if you can explain the premoistened peat moss and acidity and how that works? Thanks!

I'm obviously not Kim, but I think I can answer your questions. When dry, peat moss is hydrophobic and will often continue to repel water if incorporated dry. Premoistening eliminates that potential complication. As for the acidity, potatoes prefer a somewhat acidic soil (5-6 or so), and peat moss, with a ph of 3.5 to 4.5, is a good way to lower your soil ph if it's higher than that range. When grown in soils with less than optimal ph, potatoes are more prone to a disease called scab, which causes surface lesions on the tubers.

Lucazjay, Shazaam got it right. Peat is important to keep the pH down, but you have to pre-moisten it. Your potatoes, and your sanity, will thank you for it.

Here is a link that might be useful: My potatoes in containers

Yup, I was lazy last year and just used plain old outdoor potting soil and the results were still good. Potatoes seem pretty hearty to me (maybe that's why they were introduced all over the world to supplement wheat crops that failed).