I have a Vultr account which lets you spawn VPS instances in different countries.
I have deduced that the fastest latency would be for a VPS based in France, Lebanon seems to have an underwater connection that goes directly to France.
You can test - ping to and from their servers on this page:
http://par-fr-ping.vultr.com/
I am assuming you are interested mostly in experience for Lebanese users
There is an important geographical component to latency. If you want something global, it becomes more complicated.
There are the solutions that Joe mentioned, and there is one thing I can suggest: Cloudflare. Basically if you want something which works all across the world and don't want to bother with the technicality, you can use a CDN which should automatically distribute content for you.
.5 seconds might not make a big difference for someone who wants to buy, however I like snappy sites, I think it improves the experience, improves the image, and is better for the environment (less waste of computing power hence electricity).
A European DSL connection might deal well with a heavy site, but in Lebanon, a lean and fast site is more than a luxury. A bloated heavy site will take ages to load. But anyway it is getting better now.
There are many things you can do to make the site faster. First of all, write lightweight code, do not bundle anything unnecessary, carefully optimize photo sizes. Use build tools to minify your CSS, bundle your Javascript.
Make sure that caching is set up properly, and gzip compression is set up on the server.
I even experimented with doing Ajax tricks to get only the data that has changed. It was blazing fast. However it introduced additional complexity, SEO issues (in the past anyway - now it should be OK) and made it much harder to maintain the whole thing.
You could do something similar based on Websock, that would be even faster.
And finally use a fast platform - PHP7 on a decent VPS in Europe, or something more sophisticated (edge computing or whatever), not some crappy hosting platform in USA which is the other end of the planet.
As an example, check this site, which I coded myself, and hosted on a Vultr VPS based in London. It is optimized, but does not do anything crazy, it just loads the data through Ajax which makes it faster to browse the book catalog.
Also I used a pluggable cart (Snipcart) because I did not want to code it myself from scratch, and that part is one of the heaviest resources that the site loads (I think it is 1MB) but it loads in parallel so it would affect the experience minimally, most of the time.
There is also a "live search" function which adds to the whole experience.
Check it out:
https://dergham.com/books