Given the brand of bike (Next) I highly doubt that it has a cassette which means that it will be using a freewheel. All of the department store bikes I've worked on have used the same type of freewheel and use this style of freewheel tool:
http://www.parktool.com/products/det...=4&item=FR%2D1
You can pick one of them up at your local bike shop along with the ball bearings you need (just bring the old ones in for size comparison). A hobby shop may have ball bearings too but bearings differ highly in grade which reflects how round they are. You want your bearings round and consistent which means buying decent bearings. Grade 25 (round to 25 millionths of an inch) seems to be the bicycle standard. If your hobby shop has grade 25 bearings, there's no reason not to use them.
FYI, ball bearings won't just fall out of your wheel hub unless you somehow completely lost a cone (impossible to have happen with the wheel on the bike). Your freewheel has bearings in it which might be the source of the balls you've found. Luckily, freewheels are quite cheap to replace.