I've considered something like this but settled on ebay in the end.
I'm guessing that most people who buy second hand do so because they want a real bargain, so sales would generally be at quite low prices. The cost of setting up a website and actually drawing people in to even look at it would probably outweigh anything you'd make.
(most of the 'free' website / blog sites don't allow sales on or through them).
I think it would have to be on a huge scale to make it work - even the ebay rivals don't seem to have a lot of traffic to them.
I think it could work, why not set it up on Facebook? Loads of people have business pages, especially people doing crafty things. You wouldn't have any real costs, the publicity isn't great but other businesses will recommend your page if you do the same thing for them. This could give you an idea of how much things sell for and you can then decide whether it is worth setting up a proper business, sourcing clothes and so on.
e-bay, time is precious, that and gumtree are the only sites I use. Dont go wasting money on setting up websites. E-bay is very effiencent and it takes your money legally. You have no worries. Its already been done for you so dont make extra work.
Are there any kids nearly new sales near you? They are kind of like NCT sales but cater for older kids too. They seem to be cropping up around the country- you pay for a table and all your profits are your own. (I am in the process of setting one up in my area) Perhaps you could set up a business buying and selling secondhand sports stuff and have a specialist stall. If you started with your own goods before buying in stock then the start up costs/ risk/ time constraints would be minimal.