Most registrars offer a fairly complete DNS service. So, it's also possible to use your registrar's DNS.
You will need to add an "A" record for your base domain name and for www. (This is assuming you want people to be able to access your site using both example.com and www.example.com. The "A" record should have the IP address supplied by your hosting company.
There are some fancier DNS features that some registrars may not provide, but any of them that do provide DNS service should allow you to add "A" records.
You can also use third-party DNS, which is my own perference. There are a number of companies that will provide you with free DNS service for a limited number of domains. They are hoping that you will like their service enough that you will use their paid service when/if you grow to need multiple domain names. These are generally pretty reasonable cost.
I would definately NOT transfer your registration to a registrar associated with your web hosting company. If you get into some sort of dispute with them, they could hold your domain name "hostage".
As webwork suggested, your hosting company can probably give you the best advice for your particular situation. I would advise, though, that if they suggest that you transfer your registration to them, to run the other way and not look back.