The Economist writes from the
classical liberal perspective which is, economically at least, generally conservative (not George Bush conservative). It might not hurt to be aware of
The Economist editorial stance (Wikipedia). I'm not really all that familiar with Guardian Weekly's general leanings, so I can't really say much about that.
Generally speaking, I think The Economist is an excellent source of information (but, again, I'm not nearly as familiar with Guardian Weekly). So long as you understand what viewpoint it is being written from and keep that in mind as you read, it is quite informative.