This is a very common secured card, and one that is often recommended on this forum. There's a search box in the upper left, so you can plug in your terms to find other folks' experience. Also, head over to the credit card part of the forum to get even more details.
These cards usually graduate after 1 year of on time payments. The creditors will still do a credit check on the front end. With BoA, I'm not sure if you can apply for the secured card. I think you may have to apply for the unsecured, and then if rejected, they may offer you the secured card. I would poke around the BoA site to see what you can find.
You can directly apply for the BOA secured card. You can put down anywhere between $300-$10,000. You can do it all at once or add some along the way. From what I've read on here, it will graduate between 9-12 months usually on its own. Some call to have it graduate. They pulled Experian only for me. They charged the annual fee about 3 weeks after the card was opened. Here is more info and the direct link for you to apply from.