Hi Apostole.
Sure I can help you. I have pretty good experience. I have created https://www.serene-yachting.com/ and https://69.195.124.113/~villaghi/ (the second one is undergoing propagation in order to switch to its actual url and it is not fully displayed right now).
You actually create a website network and then you add as many sites as you like (two websites in your case, one in greek and one in english). Then you add a switch language plugin, a bit of code in your CSS folder and you are ready to go.
Before creating my first multilingual website, I tried 21 WP themes to end up with iFeature (https://www.ads-software.com/themes/ifeature). It was the only one among those 21 themes that could integrate the switch language plugin, so please use iFeature as your website theme.
The best resources are found in the following urls:
https://codex.www.ads-software.com/Create_A_Network
https://codex.www.ads-software.com/Multilingual_WordPress
https://www.ads-software.com/support/topic/multisite-in-subfolder?replies=13
https://www.ads-software.com/plugins/multisite-language-switcher/
I use either Bluehost or Dreamhost for my sites webhosting, they both work fine.
I believe you are building a brand new website. If you are revamping an old one, you will need some additional info, which I will gladly provide.
I wouldn’t mind creating the network for you, for free of course.
Cheers!
Maria