It's hard to tell what you're asking exactly.
I'm starting a new company. I am currently hosting an app on Google App Engine and want to set up a "sign up" page and start to accept Credit Card payments with Stripe. I am using a custom domain on GAE and unfortunately GAE does not allow you to use SSL with custom domains (you have to use you https://appspot.com domain, which is something I don't to do).
I am considering hosting the secure payments page on a different server
but I am not sure if this is a good option
Is that your question here, mixed in there in the middle of your post (with no question mark)?
and if it is, where the best place to host it would be.
Depends. Depends on a lot of factors. What does "best" mean? Do you think the same "best" would apply for everyone? Are you subject to specific restrictions regarding payment processing in your jurisdiction that limit your choices?
I want to keep costs extremely low and want a very simple and easy to implement solution (I just want to get something up that works and improve on it as I start making money).
I'm trying my best to avoid any fixed costs which is why I like stripe (they take a percent of sales with no flat monthly fee) and why I like GAE (free until you start getting some use).
Please let me know if you have any ideas or suggestions. Thank you.
That doesn't work well on Stack Overflow, or anywhere else on Stack Exchange. We like Questions that have Answers, not suggestions, ideas, suppositions, lists of possible whatevers that might or might not be available/useable/affordable/legal in your specific locale for your specific purpose.
Stack Overflow works best for programming questions. I.e. questions mostly about code, specific coding techniques, specific implementation issues, and the tools that go around and inside that process of producing code.
Recommendations for pretty much anything are considered not constructive, and closed as such, or off-topic if the question's purpose isn't clearly within the site's scope.
tl;dr: I'm not quite sure what your actual question is, and if it is about selecting a payment provider or a hosting service, it's not on topic, neither on SO nor on Server Fault.
You'll need to make your question more specific, and make sure it is a programming question.
If it's about whether or not you can put your payment page on a different server, I'm not sure where it could go, but it needs to be much more specific to fit anywhere, IMO.