No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
GW is a hit and miss. There is nothing to be lost. Some people have continued to send the same GW letters month after month with no success, but all of the sudden after some time....bam, they get some GW love.
By all means, it only costs you a few minutes and a stamp, so why not? Just research out if anyone else has a specific person or address that has reported success and try to use those.
Good luck