Yes it is safe to travel to Jordan - going there October and looking forward to it.
As a man, I have always gone around with long sleeved shirt and jeans. - which it was impressed on me I would have to do as I was a middle class professional.
women - something sensible - you're not going sight seeing in a bikini are you ? Being a pinko anglo I have terrible trouble with sun burn anyway
As Chris says follow Foreign Office advice on safety. Clothes, loose linen trousers or long skirts with long sleeved, high necked tops - and always carry something to cover your head when necessary.