From November 28th for 6 months, the governments of Zambia and Zimbabwe have launched the KAZA UNIVISA:

The visa is US$50 and is a 30 day multiple entry visa for both Zambia and Zimbabwe. This will also cover a day trip to Botswana; however, if a guest would like to stay overnight in Botswana then a new visa would be required upon their return.

Citizens of the following 40 countries are eligible:
Argentina; Austria; Australia; Belgium; Brazil; Britain (UK); Brunei; Burundi; Canada; Cook Islands; Czech Republic; Denmark; Finland; France; Germany; Greece; Hungary; Iceland; Israel; Italy; Japan; Liechtenstein; Luxembourg; Monaco; Netherlands; New Zealand; Norway; Poland; Portugal; Puerto Rico; Russia; Rwanda; Slovakia Republic; Slovenia Republic; Spain; Sweden; Switzerland; UAE; Uruguay; USA

A ‘ normal’ visa for Zambia is still available which is US$50 for a single entry visa, or US$80 for a double entry visa and is payable in US$ cash only. You will need to specify which type of visa you would prefer. If you obtain a double entry visa, and would like to spend overnight in Botswana, then this would be fine.