Not sure what you think is Shifty about PayPal or Google Checkout, although I have never used Google so I can't say from personal experience, but I didn't think it had a bad reputation in general.
I can give you my experience with PayPal, and to be honest I think it is great. I have never had an issue, I use it to receive payments, make payments and issue refunds, and I have never had an issue.
I do quite a few transactions a month, and I certainly don't think it is shifty, I also think it is your best bet for receiving Credit Card payments as a freelancer.
There are fees involved, but I think that is a small price for a system thats is easy to use and setup. I also use
PayMate, and give my clients the option of what they want to use. The fees are about the same, so it really doesn't matter to me.
I have not used Square before, so I can't offer an opinion on that one, but I really don't consider PayPal shifty.