Snorer, don't take more than two runners off any individual plant as you will weaken it and the runners won't be as good either (just snip off any extra ones). In general you should replace/renew your strawberry plants at least every three years using this method, although over time diseases may build up, so occasionally you have to buy anew.
If you fill 3 inch plastic pots with a soil/compost mix you can peg the runners straight into this which makes moving them much easier for both you and the plant. 
You may be best to snip off any runners until after your harvest as you will get more/larger strawberries that way. The flip side of this, of course, is that your runners won't be as well developed so you will get a smaller crop from them next year. Depends what you want, really - jam today or jam tomorrow.