First, don't take anything for granted. Check everything out from the "horse's mouth." In case that expression is too dated, it just means go to the source of the most reliable information. What any of us may say is based on our experience but remember that every business has the right to operate under its own rules and regulations (as long as they are legal). You have to verify.

My redirect is part of registration. That is normal as far as I know, but check the directions (perhaps Q&A) or ask before registration. My experience is that as a normal part of registration you are asked if you want to "park" your domain (no use for the time being), "host" (by the registrator or another), or "redirect." If you want to redirect you just enter where you want that domain redirected to. In this case, if you want to do as you say, when you register "mydomain.com" you would check "redirect" and then enter "mydomain.net." In this case you will want to register "mydomain.net" first.

As far as needing Paypay, I use it and it is good when you don't have total confidence in who you are dealing with. If you trust a host enough to do business with them, I personally wouldn't worry about directly using a credit card with them without Paypal (which they may not prefer because it costs them a fee with each payment). It is probably obvious and not too important, but if your setup is as described your host may not even know about the redirected site and it doesn't matter. Since Host Gator allows multiple sites under one plan (it appears) if another method of redirect through them would become necessary--I don't think it should--that could be done also.

Good success!

James