I want to buy a domain name, and I want to use zymic free hosting, but I don't know if its safe to go with GoDaddy? Is there anyone else you would recommend? They seem pretty cheap and reliable but idk, I'm pretty much a newb at websites... someone please help me out.

I would personally use www.namecheap.com or www.name.com -- GoDaddy is a pretty evil company.

1and1.com is also reliable. I have purchased multiple domains from them. No problems at all. Good prices too.

Don't worry. I think GoDaddy is a safe choice.