I have used at home and work 123-reg.co.uk for registering domains for years with little or no problems.

If you want a good free host, I have used FreeUK for years. There are no advertisements, no limits that I have come across in terms of bandwidth etc though I wasn't streaming music or anything particularly large. The site has about 60 to 100 pages and has about 500-600 visitors a day but used to have anything up to a few thousand visitors a day.

Depends what you are looking to do