Mainly for internet, what do you think is the minimum speed that i should get?

The real question is how much budget do you have. Computers are ALL about money. Tell us your budget we will point you in the right direction.

New or Secondhand ?

Internet can be surfed with a 200mhz machine costing under £100 but what exactly are you intending to do.

The more info you provide the more help you will get.

Hope this helps

ok im after a second hand one, as cheap as possible, if 200mhz is ok then thats fine because i intend to actually just surf on the internet mainly.
So will it be an ok speed or will it be very slow? my budget is probably around £100....

....also how much more do laptops cost compared to desktops?

£100 will buy a basic internet machine but just dont expect too much other than that. You would get a MUCH better desktop machine for the same money. A complete 800mhz machine should cost you less than £100 even with a printer etc.