Welcome!!
Firstly I will agree with Dingocat regarding the wheels. If they are those cheap ones from HF, please get rid of them. The hubs fail spectacularly at the first turn.
Secondly, if you want to do it on the cheap, then stay with a dead axle. It is already set up for you. With a live axle you are going to have to buy the axle, hubs, hangers etc that you might not need when staying with the dead axle. Also....if your fab skills (I am not sure what your level is) are not that great, then maybe a live axle might not be for you.