There is nothing bad in buying domain name and hosting package with the same provider, in as much as the provider is a well normal, reliable and has been in the business for a long time.

If you think otherwise, then you can register your domain name here: Domain name registration and hosting with other web hosting providers of your choice.

I don't see anything bad in registering domain and ordering hosting services at one and the same company.
But you shouldn't be so confident in choosing web hosting company as there are many other good and reliable.
I would recommend you to check Gigapros.com - highly uptime, competitive pricing, good reputation and skillful support.
They give free domain name within hosting package.
They can meet your expectations.

There's a lot of web hosting company that offer this kind of cheap package of domain and hosting services. I recommend you check their reviews first before closing a deal. This help you weigh and chose for the best alternative.