I would say either rent a really powerful VPS and run the API and the frontend on that server or split them up. To be honest I prefer using one server because if you use 2, you will have to do allot of tweaking to protect the site/api for xss (Cross Site Scripting) or if you use Laravel Passport and authenticate every request with a token that shouldn't be a problem.
I host my sites on a vps I rent at contabo.com I don't know how they do it but they have ridiculously low pricing for their vps's (https://contabo.com/?show=vps) you can rent a vps with a hexa core and 24GB of RAM with unlimited traffic and 600GB of SSD space for just €15 a month! And i believe that, that server is strong enough for your project.
And for configuration try http://serverpilot.io it is a great free service!