How to add Google Programmable search to WordPress
Writing it all down while it's fresh in my memory, for future reference:
How to add Google search to your WordPress website
(and Why I think that's a good idea )
100% plugin-free solution is welcome, but this is the best I've managed so far (will look into it further when I find the time).
I can't tell you which hosting to buy, but I've written in great detail about the providers I've used so far:
BikeGremlin web-hosting reviews