Hand or typewritten?
There is no particular rule on this, but generally, unless a typewritten letter is stipulated in the advertisement, write in longhand. Employers like to see handwriting and some may even analyse it. If writing longhand you will have to pay particular attention to spelling. Use a good quality pen and black ink as blue ink does not photocopy well. If you really do have poor writing or difficulty to read writing, it may be better to type it.