I think you're mis-using the term "parking". Parking is putting-up a rabbit-warren of links to try to extract revenue from a domain name that's not in use for a "real" site...
Anyway, assuming you meant "registering", rather than "parking"....
I think it's advisable to keep domain registration and hosting separate. I like to keep DNS separate as well.
This reduces the risk if you have some kind of dispute with the web hosting company. You can easily take your business elsewhere, without them holding your domain hostage.
You can reduce risk further by having your DNS somewhere other than your registrar. While rare, there have been "business situations" at registrars that have left things in limbo for months, with no ability for users to make any kind of changes. Fortunately, when this has happened, data has remained in the registries (separate from the registrar - example: GoDaddy is a registrar. .com is a registry). So, say your registrar goes bust, kuput, "off the air". The registry still has your SOA pointing to your DNS service (separate! I like dnsmadeasy...). You can still move your site to a different hosting service - say while the registrar is dead, you need to add more subdomains, need to move to a different host for cost or support or capacity reasons, etc. You can still do it. If your DNS is with your registrar, you are screwed until the registrar mess is dealt-with.
No, these things don't happen often BUT THEY DO HAPPEN. Keep registration, DNS, and hosting all separate, and you have maximum flexibility and minimum risk.
Sure, good companies don't do this. But lots of shady ones do.
Don't delegate domain registration to ANYONE. Not a designer, programmer, web host, etc. etc. etc. DO IT YOURSELF. Don't even let somebody else perform the mechanics of registration for you. If anyone offers you "free" registration of your domains, say "thanks, but no thanks!"
Use a professional registrar that specializes in domain registration. If they offer other services as a convenience, pass them up - you can probably get a better deal and better service elsewhere. If you have multiple domains, make sure the registrar is multiple-domain-friendly. For one, that means their purchasing process should't annoy you trying to get you to sign-up for additional services. And it should be easy to deal with multiple domains in their web UI. I like moniker.com.
