I’d say Namecheap. About $10 a year and their interface seems to be a lot easier to work with than GoDaddy. You’ll need that at some point to set up the DNS.
Not too sure what to recommend about the hosting service. Looked around a lot at some point and decided to set up a small VPS with a relatively unknown provider. Really cheap if it’s unmanaged and it offers a lot of control. Disadvantage (well, depends on how you look at it) is that you’d have to set it up yourself. But I much prefer it over shared hosting, the machine would be “your own” with a unique IP and no bottlenecks when you happen to be on a node where another site is drawing a lot of the resources.
