For elephants the best place is Botswana, the damn things are wandering all over the place!
The beaches can be pretty stunning all over the African coastline and there is poverty everywhere.
The country that probably ticks all of your boxes would be Ghana. I have not been there myself but they have elephants in Mole national park, rainforests and white sandy beaches. Poverty is a big problem as is wildlife conservation and you should have no problem volunteering out there. YOu could try having a chat with Ronny M, a member of TP who is secretary of a volunteer organisation in Ghana.
For your first trip to Africa, and I am probably going to be slated for this, but I would not recommend South Africa. Whilst it is a fabulous country, it has a totally different 'feel' to the rest of Africa. For example, they have a great infrastructure, poverty is there, but hidden away in places like Johannesburg. You would have to travel well off the beaten track to experience red mud dusty roads, children dressed in rags but having a wonderful time with home made toys, bustling markets, the smell of charcoal burning, baboons and warthogs wandering the streets, ubiquitous acacia trees, tribal villages complete with traditional dress and mud huts, roadside foodstalls, rediculously overloaded buses....... you get my drift? I wish I could sum up the sights, smells, sounds and the feel of countries such as Tanzania, Kenya, Mozambique, Rwanda etc. But you just have to experience it for yourself.
My second choice for you would be Kenya. Start at one of the beaches then travel up the rift valley from Nairobi as far as Kakamega to see the rainforest visiting many parks on the way including Naivasha, Nakuru etc. which are brimming with wildlife..including elephants. Any village would happily allow you to spend some time with them to assist in schools or buildings etc. A month is not long but do-able. I personally travelled Nairobi to Kakamega and back in three weeks. It was amazing and no problem in just an ordinary car.
Another alternative, but not sure whether you would have enough time would be Tanzania, the roads are dreadful but equally stunning beaches, the famous but oververly touristy Serengeti and Ngorogoro and you could continue along to Rwanda and maybe pop in for tea with the Gorillas?
Next on my list would be Mozambique (great beaches and wildlife), Malawi (beaches on the lake are wonderful)... do you want me to list all 52??
I would suggest you get hold of a copy of Lonely Planet 'Africa' and have a good read before you finally decide.
Have fun and good luck 