It is common place for web development companies to provide a service of registering a domain for you. They will then setup a website using a hosting company of their choosing. Don’t be fooled or intimidated by such kindly offers. More often then not, it will ultimately cost you stress, time and money.
The process of registering a domain is ridiculously easy. I’ve found that GoDaddy is just fine for domain 
registration despite the low-brow ad campaigns. Using the lookup, find a domain name that is available and to your liking. Select the options in the domain purchase form (including if you choose to hide your identity), enter your credit card information and purchase the domain. Be sure to save the receipt (print it out) and do the same with the confirmation email. It’s always better to be safe than sorry. Keep that documentation in a safe place along with your other business files.
Why take these steps yourself? For one, you’ll avoid any ownership disagreements. When someone else
registers your domain and is paying the annual fees for it, they may lay claim to it should the domain prove popular. In addition, you’ll decide how to pay for the domain. It is often cheaper to buy the domain several years at a time. Finally, if you ever have to move your website, having access to the domain’s setting yourself will provide this ability. Quite handy.
Hosting services really depend on the need of the website. Some websites will require a lot of server resources. Most can get by fine on a reliable shared server. Ask your developer what the requirements are (PHP, Java, Ruby, Database, Apache, etc). Then go out and shop the hosts yourself. Sometimes the registrars will offer their own hosting as in the case of GoDaddy.
Why find your own host? The answers are similar to that of the domain name registration: cost, reliability 
and control. Development companies are notorious for marking up the cost of hosting services. It’s just another way to profit from your website. At present, reliable shared hosts can be found for under $5.00 a month. Buying time in advance will reduce the costs of hosting. Some companies make the mistake of trying to setup their own servers in make-shift computer centers. These do not compare to the operations centers of large hosting centers. Hosting centers have electric failover, backups, air conditioning, fire supression and so forth.
These simple steps can save you a lot of trouble as well as money. Take the initiative and ensure the future of your web presence.