The latter - concrete byways, compacted dirt, sandy stuff. No hops, jumps etc
In that case you don't need any specific tread pattern, you can get away with a slick tyre if you rode carefullly or a semi slick to give you that bit more bite on the compacted dirt. (My Tri-cross originally came with a set of pretty rubbish semi-slick tyres on it.)
The wider the tyre the more 'cushioning' the tyre will have but generally a wider tyre means more weight / harder work.
Likewise a tread pattern will increase your grip on the dirt but it will also dramatically increase your rollng resistance.
I would opt for 'slick' a touring tyre about 30mm wide. You'll have to take the dirt sections easy but it should roll alright on the road.
http://www.wiggle.co.uk/c/cycle/7/Tyres_-_Road_City/
Sadly concrete byways tend to have a lot of glass on them so it might be worth thinking about a highly puncture resistant tyre like the Marathon+. Be warned though, they weigh a ton!