Another vote for
http://easily.co.uk/ - I've been using them for several years now without problems.
For web hosting one can either use their hosting, redirect to another domain, or redirect to another domain using frames to "hide" the redirection(horrid, as ferret said).
For mail you can set up a "catch-all" email address, and all mail sent to the domain will be redirected to that address. This allows you to have unlimited email addresses for that domain, as they all just get sent to the alternative address you specify, where you can then filter them based on the original intended recipient.
They've recently tidied up their control panel, making it easier to use, so all the stuff you want to do should be a matter of minutes to set up (including registering the domain and making payment).
You can also change the nameservers for the domain (while still having the domain managed by Easily for renewals and so forth), which could be useful if in the future you want to host the domain somewhere else in its own right, rather than just forwarding to another domain.