A microphone jack plug should be able to connect straight into a socket provided on your computer.
There are many microphones that will do the job amicably, and well below the £40.00 range.
An adapter would be ideal, for connecting a number of devices, and Maplin's may have the answer there.
If you are thinking of 'producing' your own music, then there are package deals available, which consist of software, adapters and leads. It's just a case of plugging in the guitar lead (if electric) or plugging in the clip-on pick-up device or microphone. Set up the software and away you go, in mixing and recording.