Here is a video I made last week in which I and a colleague discuss websites for newsagents and how the newsXpress / Tower partnership delivers.
Being online is critical, but maybe not for the reason you think. People use websites to browse. Not being online means you’re not reaching those browsers. I have heard of people driving hours to pickup something they found online.
When people search online they are searching for an outcome, not for a business. Think on that … many small business retailers go online with the goal of making their physical business easily found. My advice is focus of what the shopper wants, what they will search for.
The other comment I’d make is you are not your customer. What you might do re online shopping is not what others might do re online. I would never have any retail business today without an online presence.