Second the AT2020 it's a good place to start.

EDIT: If you don't have a interface (Which I'm assuming you don't) it might be best to start with a usb mic or look at expanding the budget a little and get an interface with it. The AT2020 does have a Usb varient but it exceeds your price range.

I know this is out of your price range but this is everything you would need, with upgrading in the future being an option. If you bought a usb mic now and wanted to upgrade to a xlr mic later you would need to by an interface on top of that mic anyway. Just something to be aware of.

https://www.amazon.com/Focusrite-Scarlett-Studio-Interface-Recording/dp/B01E6T54E2/ref=mp_s_a_1_6?ie=UTF8&qid=1541401196&sr=8-6&pi=AC_SX236_SY340_FMwebp_QL65&keywords=focusrite+recording+bundle&dpPl=1&dpID=41K2dCwPdgL&ref=plSrch

I'll always say to start off sitting in your closet to start.

If you need the whole kit, there is a combo

https://www.amazon.com/Focusrite-Scarlett-Studio-Interface-Recording/dp/B01E6T54E2?ref_=d6k_applink_bb_marketplace

Otherwise the focusrite interface is a good start and then the audio technica at2020 or the Shure sm58 are good xlr mics to start on.

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.