What would be the best way for an indie guy with a budget hosting to share an interesting article?
Publish like normal and accept that, if simultaneously on Slashdot and Reddit, you're doomed. If "doomed" is not an acceptable outcome for your online presence or if you have a greater-than-epsilon chance of going viral, don't use budget hosting. (Better options include a VPS or hosting environments which are not bottom-of-the-barrel.)
What would be the best way for an indie guy with a budget hosting to share an interesting article?
Amazon Cloudfront with the cheap hosting as a custom origin. Use a CNAME like cached.domain.com and share that link. If the original link gets shared, you could at least change the links to images, css, and js to the cdn copy.