As johan rebel has mentioned late March is the end of the wet season and as such your game viewing is not going to be as plentiful as it would say in September or October. He also mentions that Chobe can get very crowded. There are a number of large lodges on the banks of the Chobe River which attract tour groups, as well as a large number of day trippers from Victoria Falls. As most of the accommodation is centred in the same area, most of the safaris all take place in the same limited circuit, adding to the very busy feeling. Having said that, Chobe is a great reserve, and if you chose carefully can be a great experience. I would personally recommend Elephant Valley Lodge, the main reason is they invert their safaris to run contra to everyone else. So while all the other lodges do an evening boat safari and a morning 4x4 drive, EVL does a morning boat safari and evening 4x4 safari drive. The result is that you have a far more intimate experience on all your safaris.

Hwange would, however, be my personal recommendation. The transfer time would be longer (to reach the southern private concessions) than to Chobe, but at the end of the day and extra hour or so per transfer is not much of a sacrifice for a better experience for the entire safari stay. With your budget description I would probably recommend something like Bomani Tented Lodge.