The obivous thing to look for in this case is: Viewing angle.
One thing that is special for your use case is, that you will need to focus more on vertical viewing angle (which, in the case of a portrait oriented monitor, will be the 'de facto' horizontal viewing angle).
From the wikipedia link above:
The viewing angle is measured from one direction to the opposite, giving a maximum of 180° for a flat, one-sided screen. Some display devices exhibit different behaviour in horizontal and vertical axis, requiring users and manufacturers to specify maximum usable viewing angles in both directions. Usually the screens are aligned and used to facilitate greater viewing angle in horizontal level, and smaller angle in the vertical level, should the two of them be different in magnitude.
Also, from this article, consider the size of your screen relative to viewing angle and viewing distance:
IPS monitors will also show color and brightness shifts from edge to edge depending on the quality of the display, it will simply be less than a standard TN display. Here is the same illustration, this time showing our Apple MacBook Pro 15″ Retina display at a standard viewing distance. Notice that while the color shifting is more subtle, we still see a significant amount of shifting in brightness from edge to edge.
So I would definitely recommend you to look for a monitor with an IPS panel and as wide as possible vertical viewing angle. Some modern displays will have very wide viewing angle up to 178° / 178° (for example on a Dell U2414H, which also has a very thin edge, enabling you to mount two of them very close to each other.