Help: How to avoid first traffic surge crash

Hi folks,

I am about to launch a small saas website, and hopefully there will be a surge of users if it proves popular.

Would any of you be able to offer advice on what is the best cheap method of hosting so that if a lot of users visit at once that the site does not go offline?

I host a few small blogs on bluehost, but for this type of saas site, should I be using something like AWS?

Thanks for any advice you can offer.

Ross.