I got a kohls credit card when I first started building mine up. I like credit karma. I actually have several credit cards I just don't use them alot. Maybe $20 here and there and then pay it off. My hubs got a personal loan with me on it and it bumped our credit like you wouldn't believe. Just got better when we paid it off.
I like capital one quicksilver one for a first card. Nearly everyone gets approved. 6 months after that they will increase your credit card limit and then I would get some sort of retail card. I did Walmart, my sister did meijer. In order to help your credit they do not want you to pay it off every month. Pay it down to leave a balance of 30% of your limit. If your limit is $600 only pay it down to $200 every month, of course still always pay at least your minimum due.
We got a credit card through our bank instead of a loan and we put it it in both of our names and every time we pay on it , the money just goes right back in there as useable funds Incase you need it again, AND it makes our credit shoot up. My score has went up 114 points since March.