Is Thunderbolt 2 equivalent to Mini-Display port?? Both physically and technology standpoints??

As was noted, Mini DisplayPort uses the same connector as Thunderbolt I/II and any Mac with a Thunderbolt I/II port can output to a Mini DisplayPort or DisplayPort (with the right adapter) monitor. There are also some older Macs that have a Mini DisplayPort only where the connector will not work with Thunderbolt.

If one needs Thunderbolt, it requires a Thunderbolt specific cable. People who have bought Mini DisplayPort only (i.e. video only) cables found that they didn't work with Thunderbolt devices. There are also some Mini DisplayPort to DisplayPort cables that won't require a separate adapter to connect to a DisplayPort monitor input.

No Thunderbolt 2 is not equivalent to Mini-Display port.

But they use the same connector.

And thunderbolt 2 on mac can output mini display port signals

Thunderbolt can do a lot more than just displaysport though

But to answer your question, Yes you can use a minidisplayport display,

You can also use other ports with the correct adapters:

About the Apple Mini DisplayPort adapters - Apple Support

Good luck!

Since you already have an HDMI output, you should just get a monitor with an HDMI input. Using any of the other ports can take away from them if you need it, since usb and thunderbolt can do data-transfer but HDMI cannot, and HDMI is solely for transmitting video signals.

As for specifications, it depends on exactly your needs. I'm not sure what Mural is, but based on it's name I assume its some kind of art-based application. As such you may be interested in a monitor that has an IPS panel (better colors and viewing angles). You'd probably do fine with a 1080p monitor but you can go higher if you wish (that's just more money). For brand, I'd say just go to Amazon and check out the ones with the best reviews and, if possible, see if there's a tech store near you that may have them on display/offer and check them out in person.