Blue barrels will work fine

I’ve even seen them growing in vertical PVC tubes. There are quite a few variations on the theme of “how”, so perhaps the best option is to Google “strawberry barrels” and see all the different links and youtubes that come up. More than a few are using those blue barrels.
As for variety, I don’t know that I’ve ever seen one variety rated over another in terms of growing them vertically. What I have seen is which varieties are more/less resistant to whatever temps, bugs and/or diseases you might have in your local area. That would be the more important consideration. Your county extension agent (particularly their on-call Master Gardener) should be able to answer which varieties do well in your area.
Our strawberry bed got off to a really slow start, mainly user error (mine!). But this year we’ve got a nice strong bed of young plants out there and I have high hopes for a good crop. Yum!