Basically any monitor that you can mount vertically will do, doesn't need to be special. By default, TN are generally setup so that horizontal viewing angles are better than vertical viewing angles because they're wider so they need to be, and this means if you turn it vertically it will still work well in that axis, so long as it's pointed at you. If you get a VA or especially IPS then there also shouldn't be any issues in that regard.
Cheapest option is probably to get the cheapest monitor you can find with a VESA mount, and then a compatible arm. Or, if you get lucky and find a cheap one with a fancy stand built in, that could work, but generally more advanced stands are reserved for higher end monitors which are going to cost more than you need to spend for this.