Why dont you start with cha-cha and rumba in the latin and Foxtrot and Tango in smooth.
If you can do the cha-cha good, you will not have any trouble with mambo. The rumba make you do the cuban motion right, which you'll have to apply for all your latin dances. Salsa can be complicated when it comes to footwork, can you do mambo you will have no trouble with salsa. If you do the samba, start practicing this when you are ready for mambo. Swing should be started as early as possible, does not matter what type it is. This is a dance which I use as a "dance down dance", that is always put in a swing at the end of my practice. Because of this, swing is my best dance and I am SO relaxed when I do it.
Foxtrot will make you get the right attitude in smooth, and you can dance in a nice not too fast tempo. Remember, foxtrot is all dances mother. As for walts, not that different from foxtrot (for a beginner) much of the same concepts but you'll have to add rise and fall. Tango is very different from the other ones, but will give you good practice in walking which is important in smooth. Leave quiqstep an vw to the end. When you know the otherone reasonble well, practice the quiqstep, it is fun, but can be dangerous if you do not know it well.
But, you'll have to have fun to be good. If you do not like it, leave to next time and practice something else. Good luck!!