Some things to know before you go:
BEFORE YOU GO
It is expensive. There are only two international flights a day into Victoria Falls, Zimbabwe (VFA) - both go from Johannesburg OR Tambo (JNB) and arrive around the same time (just after noon) and fly out of VFA back to JNB around 1:25 PM. Hotels are also very expensive. We stayed at the Kingdom for $180/night. If I paid that much for a hotel in the US of that quality, I would be furious. Remember that you are in a beautiful place and just be prepared to spend a lot. US citizens can get a visa upon arrival - check your country's requirements.
NOTE ABOUT CHECKED LUGGAGE
I don't know about British Airways but South African (Flight 40 is JNB to VFA and 41 is VFA to JNB) uses an Airbus 319-100 and the staff is extremely surly and will make you check-in even normal carry-on luggage. Two members of our party had their locks broken and one of these two people had items stolen from their bag.
GENERAL FLIGHT NOTE
A sandwich is served from JNB to VFA and proper lunch is served from VFA to JNB on South African Airways.
A single entry visa is $30 and a double entry visa (necessary if you want to cross over and see the falls from the Zambia which I highly suggest you do) is $45. Make sure you state this clearly upon arrival and fill out the correct form - there are only 2 guys doing Visas and the line gets very long very quickly. Everything is done in USD so there is no need to change currency.
AIRPORT TO HOTEL
If you have a group (namely, you are not a solo traveler), don't bother with the $10 - $15 pp transfers done by the hotels or companies like Shearwater. Just negotiate with the guys in the taxi line. We got one direction for $25 and one direction and $20 in the other.
This is an absolute must-do. The rates are difficult to negotiate but a sunset cruise through a reputable company like Mapopoma (sp?) or Shearwater should be $42 - $45 pp and include pickup from your hotel at 4 PM with unlimited drinks (alcoholic and non-alcoholic) and snacks.
VIEWING THE FALLS
If you can, get a double entry visa for Zimbabwe ($45) and then you can walk across the bridge to Zambia and get a day tripper visa ($20). If you don't want to do the long walk, you can do a double cab (one cab takes you from your hotel or the Zimbabwe park entrance to the Zimbabwe border and another one takes you from there to the Zambia side) for $15 or so - negotiate the price!
I would suggest viewing the falls from both sides. It is a different experience and on the Zambian side, you can see the falls from below at Boiling Point (be prepared for a strenuous hike). I would give yourself 3 - 4 hours for the Zambian side.
Park Entrance: $30 for the Zimbabwean side (2/3rds of the Falls) and $20 for the Zambian side (1/3rd of the Falls). On the Zambian side you can also easily walk along the side but please note on the Zambian side, there is a dearth of fencing so please be careful.
If you are really lucky, you will be there at a time when thee is a full moon and you can do the night moon rainbow.
Zimbabwe is not dangerous (except getting. We were prepared for who knows what. People are extremely friendly and there are green uniformed Tourist Police everywhere - they are happy to escort you anywhere you go. Even the vendors who appear literally out of the bush are not too aggressive. They will all try to sell you the same "Happy Family" statue. Do your shopping on the Zambian side if you can as the quality of the art is better and more unique.
Make sure you have lots of cash as very few places accept a card.
The falls are amazing. You will love them.