Your first purchase should probaly be a revolver.It should be of one of the types listed here. You will probaly want more than one, BUT start with one,get the other weapons you will need, then go back and get more revolvers if you so choose.

.

The second weapon you will need is a saber. It can be obtained reasonably and NEVER RUNS OUT OF BULLETS !

The next weapon you will need is a carbine or rifle. Most cavalry engagements were fought on foot and you will need a long arm.