1&1 is not owned by EIG but by United Internet. However, they are about as bad as an EIG owned hosting company and I would avoid 1&1 unless you have a desperate desire to have a potential nightmare experience. 1&1 is horrible for over billing, billing even after you leave or cancel your service with them and they have a wealth of other bad nightmare issues that many customers have had to deal with. Do a Google search for 1&1 and scam, nightmare, stole, any other bad word and you'll see what I mean.
GoDaddy is another I would stay away from as they give much lower resources than most hosts in the same price range and you'll constantly be getting warnings about exceeding your resources and you need to buy more. They are ok for a small site with little traffic that has a lightweight site on it but there are much better options out there for hosting.
You can check out our hosting section of the forum and there are several great choices there. If you don't see anything that fits you need then you can also try Namecheap hosting. I've used them as one of my hosts for a few years and they are great. Their support has always been awesome to work with and I use their support for all kinds of needs and they have always been super.
Other than that, there are several good hosts out there, you just need to do some research before committing to a host you don't know. I would also HIGHLY recommend not using an EIG owned hosting company. They are the worst that I have ever used and they tried on 2 different occasions to extort me out of more money and kept me from accessing my sites for a few days at a time. They also have the worst tech support i've ever dealt with.