If DNA testing is to be used for legal purposes the lab that is to do the testing has to be satisfied that they samples have been collected and handled in accordance with strict procedures, so that no tampering with results is possible. That means that its best to find a lab first and let them arrange the sampling procedures.
Typical fees for paternity testing (to legal standards) are around �400 but such fees often exclude payments to the agent carrying out the sampling (such as a doctor). If you google 'DNA tests' you'll find labs offering services from �99 upwards but many of those services might not meet the testing requirements necessary for submitting evidence before a court of law.
This link goes to a commercial site. I'm not recommending this particular service (because I simply found it on Google) but the link does provide further explanation (including about the differences between 'legal' tests and the cheaper 'peace of mind' tests):
http://www.dna-bioscience.co.uk/service_court_ paternity.shtml
Chris