Ah, I see. Well based on your requirements, I wouldn't worry too much about the processor as you will probably not notice much difference in speed.
As for speed, I would focus on RAM and storage.
RAM pretty much is a fast storage space for small items like opening programmes, etc. I currently have only 4GB and have no issues opening programmes or large files. Mind you, I'm not doing gaming or large video editing.
Storage will be either HDD (Hard Disc Drive) or SSD (Solid State Drive). HDDs are less expensive but slower. SSDs are just the opposite; however, you usually spend over £200 with SSD computers that you can purchase off the shelf.
I just did a search and found >20 which have 4GB RAM, <2.5kg, <£200, and a sizable HDD for what you'd need in storing music, videos, etc.
Is this kind of what you were concerned about?