Joining the Zidagar will have no effect on whether or not you can join the Voinians, but it's definately not the easiest or quickest way to make money to get a good ship.
One way you can quickly get the money you need is to go to a system along the border of two of the strands, preferably one with an uninhabited planet that you can land on. (I think either the Grooz or Vastan system works well for this). Anyway, you should find that both Zidagar and Igadzra ships appear in the system, and proceed to blow the heck out of one another. Wait until one side disables a ship on the other, and then board it and steal it's credits (If you're feeling lucky you could try and capture it as well, and maybe have your problem soved right then and there, and have something to post about in the "One Lucky Capture" message!). This would work extremely well with Azdgari vessels too, their warships can carry upwards of 300,000 credits for you to steal. And all you have to do is wait for the other strand to do the work for you!
Note: If one side completely overpowers the other and destroys all the ships before you get a chance to board them, land on the planet (that's why it's helpful to have one in the system) and then try again. Repeat as needed. Then run off with your excessive amounts of credits, laughing maniacally.
-Thunder
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Do not taunt the Happy Fun Ball. If Happy Fun Ball starts to smoke, run away and take cover.