I realize that this question is being asked in a very generic fashion, without detailed specifics of the configuration in question, and thus I am not expecting answers that go beyond anything but general guidance.
With that, given a WordPress site that is:
based on a typical "heavy" ("kitchen-sink included") theme, purchased via ThemeForest.net, and
hosted on typical (entry-level, Linux-based) "cheap hosting," priced at under $10/month
... to what degree can one realistically expect that the use of properly-configured caching-plugins (such as W3 Total Cache) and a CDN solution (such as CloudFlare or MaxCDN) can significantly boost the sluggish performance of the current setup?
In other words, if we take as an upper limit the performance that might be achieved hosting that very same website on a "high-end" hosting package (say, WPEngine's "Professional" plan, at $99/month, or even their "Business" plan, at $249/month):
Is there any realistic chance of achieving relatively-"zippy" performance despite the underlying "heavy" theme and relatively-weak infrastructure of the cheap hosting?
Specifically, what ballpark percentage of "high-end" performance might realistically be achieved?
And what estimated plugin- and CDN-related expenses would be required each month? Also: what ballpark percentage of peak performance might be achieved using only a "free" CDN plan?
Primarily, I'd like to receive -- if possible -- a "sanity check" that at least a "semi-respectable" level of performance can nevertheless be achieved with cheap hosting in my situation, with the proper tuning and external support (as well as general guidelines on the direction to take).