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I started out with the same issue - I moved to the US in 2011 and had zero credit history and a very vague understanding of what a credit score even was.
My first secured card was a BoA with a $500 deposit/cl and a $39 AF. I applied at the branch, and the manager recommended that I go for one of the cash back cards and not just the regular secured one, which I did and got approved. I cancelled that card after the first year, since they wouldn't give me a CLI (can't really fault them, since I had pretty much no income coming in at that point).
About 9 months after I opened the BoA I tried applying for a Chase Amazon Visa and got denied due to "insufficient history", so my boyfriend opened one for himself and added me as an AU. Around the same time I added one of the "Shopping cart trick" cards.
Fast forward to 2013 - I got three instant approvals for much nicer cards (BCE, Freedom and BoA TravelRewards).
I'm also not sure that you will be able to convert to prime (or even get the card unsecured) after only 6 months, if you have truly no credit history. The standard period of time to get the card unsecured is around 9-12 months.