Connecting visa HDMI should be fine.
But I think it would help if you provided more information about your needs.
Eg., what sort of budget are you working with? What do you need the displays to do? Are they just going to be used for simple productivity stuff like web browsing and office apps, or are they to be used for design work where things like more space, more pixels and colour accuracy are important? Does your school have existing procurement contracts? Where in the world are you based (costs and availability varies quite a bit)? Do you want like-for-like 27" replacements, or would you consider other sizes? Etc.
There's a whole world of monitors out there, from simple generic ones that cost $60-100 to far more specialised expensive ones. I would start by defining your needs rather than just asking for random recommendations.