Whilst I'm not a 'success' story yet (well, certainly not in the wider view of the term - but I meet your modest criteria!), I lost my job a couple of years ago, I couldn't get another job, so started up a company in Feb 2013, just finished Y2 trading....£205k turnover (not bad turnover from a standing start after 2 years), approximately £70k pre tax profits ...and still growing fairly well.
i'm still 'small' based out of in my dining room (which now looks like something like the flat in only fools & horses), but I'm starting to outgrow it...just waiting until that point where it's totally clear that I have to move into proper premises (I'm very reluctant due to the extra cost ...& security worries)
The secret (IMHO) is to find a niche/under-represented area, then throw your heart & soul into it...build sales up to a level where you can gain a supplier's trust ....and ultimately hopefully supplier exclusivity (which I now have). This isn't going to work for those products that you can already buy here in the UK (via Ebay/Amazon overseas sellers), you have to find a niche & go with it.
the biggest challenge? Well aside from finding something that sells that nobody else sells(!), the biggest challenge is working out which 'software tools' you need, & then of the tools you need, which are the best for the way you work ...then once you've decided on the best tools, then working out how to glue them all together to make a slick operation ...e-commerce in 2015 is still very fragmented from a 'systems' point of view.
Also everybody wants a piece of you ...so dodging all the burdensome monthly subscriptions is quite a challenge (for example - everyone bigs up cloud accounting packages ...such offerings are spawn of satan in my books, buy last year's desktop version on ebay for £80 & you're good for a few years with that, etc.)