Unless you don't care about SEO, i.e. shop indexing this is a 'very' bad idea.
Else you will want someone like presta4you.com to create a custom solution....
What you are looking for is 'onboarding', i.e. when they register then they run through an oboarding of what categories they are specifically interested in, working how how to display to them 'only' those categories is tricky...probably create a 'private group' of 'one' which is only associated to those categories, edit caregory scroll to bottom. But if you are expecting 1000's of these they may not be manageable. It will be interesting to see how your theme will handle that...let alone menu system (they are pretty dumb)....
best advice, look at your competitors, do they have that feature? do they have other features you do not have (get those)
good luck...