Cross bikes will handle all sorts of stuff. However having no suspension and low volume tyres means it's rough going on the bumpy stuff. Although the wheels are plenty strong enough, the smaller tyres means the rims are more vulnerable to being bashed and bent on the rocks.
The big difference between riding a mountainbike and a cross bike on the rough stuff is the speed of the transition from 'challenging, but okay' to 'I think I'm going to die'. On the mtb you have far more time (because of better brakes, tyres, grip, suspension, handlebar width, etc) to get it all back under control. On a cross bikes it's all okay one minute and then it's just, well ... all over.
So although a cross bike seems like a 'jack of all trades' I would think carefully before going down that route. If you have a mountainbike I would supplement it with a pure road bike.
And getting a road bike doesn't mean you're no longer a mountain biker. It's not an 'either / or' situation . Lots of us are both. I would even argue that you become a better rider all round if you do both. Certainly you will be a much stronger, fitter cross country mtb rider if you get the road miles in, especially during the winter.
So if you have some idea what you would like to do with the road bike, it helps narrow down the options (within a given price band). If you want to ride in the winter when the trails are at their crappiest (this summer excluded), then what is called a 'winter training bike' might be quite appropriate as it is a race style bike, but can take mud guards. Although not essential they do make foul weather riding more tolerable.
However if you have a lack of 'intestinal fortitude' and only ride in the dry, then any 'race bike' will do just fine.
Ribble Cycles do a winter training bike that is good value, as are their road bikes. (Their shop / mail order service is however 'variable'). You are right to think about a minimum acceptable groupset, however with a road bike, the frame has more of an influence on the total 'ride' than it perhaps does with mtbs, where the fork is perhaps more important. The bits on a decent frame can be upgraded, but a crappy frame will always be a disappointment.
I think 600 quid is a significant price point. Here you will get choice from both the big bike companies and your independent bike shop. This should get you a reasonable frame and wheels with probably Shimano Sora or Campagnolo Mirage or even the slightly better Tiagra or Veloce componenets.
Remember proper fit is important on a road bike. A decent shop will get you set up properly with the right stem and bar width, etc, at no extra cost. Buying 'on -line' or through a super market will mean you will be responsible for swapping these bit if necessary at your cost.
Depending on where you live, lots of people on here will be able to recommend good shops. If you're in NW England, Hewitts in Leyland is a no brainer. But don't over look the French sports store '
Decathlon' if they have one of their ever increasing number of stores near you. (London, Essex, Stockport, ???)