Actually, only the first time that you ever apply for a visa, you are fighting the quota. Then onwards, you are just reusing the same number - so no worries there. [this is good until the 6 years of eligibility of h1].

Secondly, if your application had been pending for more than year, then you can keep your h1 alive (even after 6 years), and use your pending-gc-application to get h1-renewals.

Lastly, if you get past the first two and a half stages of the greencard process and you get an EAD and you have worked 180+ days with your employer, then, as Southwest says, you are free to move about the country. :)