If you are looking to pass it off as a diamond, please check some of the diamond websites for what you could realistically afford then find the same in the material you would prefer. Preference in material, which it looks like Asha fits your bill, is yours alone.
What you say is again, entirely your own, with "I got a great deal online" as my favorite
The cut preference, you have to narrow down. I think you'll find people on here who like each of those cuts. Now, there is an antique cushion
as well as a more modern cushion
Which looks better will be your decision and also might look better in particular settings.
You might want to start with what kind of a look you are going for? Halos are popular now, "plain" solitaires don't have to be "plain", and there are any number of side stone options. It can become overwhelming. Since it looks like you like something "not round", how about trying to narrow now "more stones" in the setting or not?
There really are SO.MANY.OPTIONS. including custom.
If you can decide what color you like (warmer like J, or cooler like F) that will help you a bit as well.