I run a pro audio company as well as owning a studio. The primary thing for a live rig would actually be speakers and not signal chain. If the speakers can't do it right, the signal going to it gets compromised. The second most important thing is the console. Your system will sound better as a whole by putting a decent front end on it rather than buying individual pieces (you will get a lot more improvement out of a console investment than a bunch of pieces). Third is your system processing. Its amazing how much people overlook what a good system processor will do for their sound. Fourth will be mics. Some may argue that mics are more important than 4th, but if the rest of the system can't accurately translate the signal, than the mic is being wasted anyhow. If your system can't sound good for vocals with an sm58 through your console with only minor EQ'ing, than the system is spec'ed or set up wrong. It always amazes me how many venues I go into and find out that they have decent gear, but such a poor implementation that it is all being wasted. Some of the bands that I mix for like to tease me and tell me that half of the money they pay me is for mixing, and the other half is to rewire the venue and set their system up properly.
If I were you, I would save up for six months and get equipment that will be worth keeping and not blow your money every month on little pieces. If you do that, before long you will have a cheap system that doesn't work much better and has no resale value. If you get the right pieces, it can stay with you for years, and if you do need to sell it, you will get more back from it.
