I want the api to be as quick as possible so I want that well away from the back-end server.
Is the API a completely separate application.
Otherwise there is no such thing as having the API well away from the back end.
The back end is where data is derived from and sent via whatever means.
And the front end I'm not quite sure I understand.
A front end is basically nothing but static data until you do something with it.
For example take the page you are looking at right now on this forum.
Okay now take a reply in the text area. It is nothing but a text box sitting in the browser doing nothing.
The back end comes into play once you hit that post button.
Basically a front end is meaningless in that it doesn't matter what you use for a front end it boils down to it's always HTML.
You can choose from all types of various packages, libraries for front end tooling, but it's still just static data waiting to be acted upon.
Many folks get confused between the terms front end versus front end manipulation. In which front end manipulation has a lot and more to do with looks and feel, but has little or nothing to do with the actual data sent to the back end to be inserted or updated, whatever the case may be.
You could have a plain Jane front end kind of like the out of the box laravel login or all types of Fancy controls, dropdowns, sliders, some pretty widget, or whatever, the back end and the database could care less about such things, its goal is to Crunch data not be pretty.
So in my opinion your main first goal should be concentrating on an efficient database manipulation and management system, not a pretty front end, that can come later.
As far as hosting you probably need dedicated servers with load balancing. Is it a big enough company to have their own servers.
But for a business application I wouldn't try at first to set all this stuff up yourself, either hire a consultant or see if your dedicated server company has experts to help set this stuff up correctly.
I would not just trust any Forum answers on this, get an expert.