I guess you are probably interested in the northern Cairngorms, accessed from the Spey Valley, rather than Deeside or Glen Shee?
The most convenient, if not necessarily the nicest, place to stay is Aviemore - will you have your own transport?
Ben Macdui is perhaps the classic outing in the area:
https://www.walkhighlands.co.uk/cairngorms/macdui-cairngorm.shtml It's at the upper end of your distance/height gain requirements and require careful navigation in poor weather.
Meall a' Buachaille is good option if the cloud is down on the higher summits:
https://www.walkhighlands.co.uk/cairngorms/meallabhuachaille.shtml Sgor Gaoith is another nice possibility:
https://www.walkhighlands.co.uk/cairngorms/sgor-gaoith.shtml I think the biggest difference you will notice from what you are used to is the lack of trees (the tree-line in Scotland is at about 400-500m) and the lack of any waymarking on high ground. On the high Cairngorm plateau, poor visibility and strong winds are common, and the featureless stony terrain means it is quite easy to lose the trail in places - solid navigation skills are necessary!
Hope you have a great trip!