Hi,
You didn't say whether you broke it through misuse i.e. you dropped it. If it has just stopped working you may be able to get the retailer to fix it for free.
If my iPod were broken and I couldn't get a repair for free under SoGA I would send it to Apple as they are a trusted and credible company, will give you a warranty and you can be sure that they are using genuine parts.
You may find someone cheaper services on the Web. If you insist on going down that route make sure that they publish an address, have terms and conditions. You can give yourself
additional protection by using a Visa card to make a payment. If they don't accept Visa go elsewhere.
Watch out for companies abusing the intellectual property of Apple in their domain names and company names. Although this may not affect the service, it indicates that the company may be ignorant of the law and may have similar scant regard for your statutory rights!
This may be of interest:
http://whatconsumer.co.uk/forum/technology/7781-ipod-repair-http-www-cheapappleipodrepairs-webs-com.html