No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Double check on the IRS web-site to be sure, but I just looked at this not long ago myself and believe that it doesn't matter who paid the point, as long as it is on the 1098 or HUD-1 you can deduct. The best course of action would be to contact a CPA to be sure though.
I think IRS publication 530 has what you are looking for.