It may seem strange to you at the moment but the slow dances can be more difficult to learn than the quick ones because they need better control of your balance and body movement. You will develop this as you dance more.
I would strongly suggest you learn from a qualified teacher and a group class is probably best to start with. Each dance has some similarities to other dances. What you learn in one dance will be useful when learning another so it is usual to learn a few dances at about the same time.
Your teacher will have a preferred order to teach the dances and the figures within them so I would go with the flow. Personally I would start with waltz, social foxtrot and cha cha, followed quite soon by quickstep and rumba. These can be developed together for quite a while before adding any others.
Do not wait to master one dance before learning the next. It can take forever to really master a dance.

Whichever way you choose, enjoy yourself!