The Ortlieb panniers that you linked to are the ultimate in waterproof panniers. Although their waterproof-ness cannot be questioned, some people do criticize them for generally just having one big compartment, and no smaller compartments or divisions to help organization. However, they have addressed this concern with some of their newer designs,
like this pair.
Another alternative would be to get a set of regular panniers, which do generally have side pockets, lid pockets, etc., and then buy some rain covers to put on when the weather is bad. See
this set from a Canadian camping store. This is what I use, except that my rain covers are flourescent yellow, which is a good idea because if it is raining then visibility is probably reduced.
However, I also have a pair of the Ortlieb front panniers (
see here). I originally toured with front and back panniers but have since learned to carry less stuff, and so only need the rear ones. However, I use one of the Ortlieb front panniers on my rear rack as a daily commuting bag or a day pack on a long ride, and it is awesome - I've been using them like this for 10 years now without them showing much wear!
Ortlieb also have a very good attachment system which will work on just about any rack, stays on very solidly when riding, and is easy to take off and put onto the rack. This is another very important attribute to look at when buying panniers.
If you're not camping then 40L should be more than enough - even when camping I can keep it down to a pair of 40L bags plus tent and camping pad strapped to the top of the rack. The amount of clothing is similar to what you stated, plus I have cooking gear and a sleeping bag to squeeze in, so you could certainly switch all that for a small laptop if you so wish (although I wouldn't).
You asked whether the waterproof overtrousers are necessary - I would recommend that you get a pair or at least something to wear on your lower half in the rain. I have a pair of cycling pants that are waterproof on the front side, and are just spandex on the back - they keep me mostly dry and I never overheat. Obviously, a good pair of fenders/mudguards is essential to avoid the water coming off of the rear wheel and spraying the back of your legs. Make sure that whatever you get it is very close-fitting around your legs, otherwise it will be very annoying while riding.