Hello mate!

From an absolutely newbie point of view looking to record some vocals and a guitar can EASILY be done by 'just plugging it in and starting to record.'

You need a Laptop which you have, some software like Audacity (which is free) some headphones, and a microphone.

The microphone you posted requires an audio interface with phantom power which will cost you somewhere between 50-100. Considering its not a very good microphone I would recommend looking at either:

USB microphones for ease of setup, no additional hardware needed like this-

https://www.amazon.com/Microphone-FIFINE-Computers-Podcasting-K670/dp/B079HRFH2Y/ref=sr_1_10?ie=UTF8&qid=1538688598&sr=8-10&keywords=usb+microphone

OR

A bundle with everything you would need to be a bit more serious like this-

https://www.amazon.com/Focusrite-Scarlett-Studio-Interface-Recording/dp/B01E6T54E2/ref=sr_1_10?ie=UTF8&qid=1538688671&sr=8-10&keywords=microphone+bundle

There can be more complications if for example you want to record a podcast in the same room to the same laptop.

Those links I posted are examples, not recommendations. If you can give some more information on your likely setup, your laptop specs, any software you've used before, any other hardware you have (like headphones), your budget etc... I'm sure someone could give you a better answer/recommendation.