I have recently been tasked with the same thing. I am going to suggest a whole new org website (to help manage membership lists, etc...) since ours is a mess and unmaintainable. So far, I like
http://groupspaces.com and I want to look into more.
Also, Paypal is a good option because it doesn't make you sign up for an account if you are just paying someone via cc (one-time payment).
No matter where you go, there will be fees to accept payment, so I hope they take that into consideration when allowing people to pay online.