For a beginner & only one month left you will have to be very dedicated in feeling confident in using a mouth reed or diaphragm, they are both the same thing! Yes, a single reed will be able to do all the sounds you mentioned & more, it's all in the practice & using the right reed for a newer caller.
Stay with a light tensioned single reed call, there's no need to go with a double or triple reed it will only take you longer to master & you will be limited in quality sounds!
Some of the best to use are Mellow Yellow & All Star reeds, they are lightly stretched latex & are very user friendly, you will learn quickest with this type or anyother lightly stretched single reed!