Hi nice to meet you.
Your organization is having problem with customer's sign in and purchase system, in that case I found an solution for your ORG. Upon further analysis, the problem can be solved easily but it would take a little time. Let me explain to you :
1. A Landing page must be needed to show your professionalism and an Opt-in box required to make friendly your customer's Login.
2. As you said a auto password generator will be setup for your customers so that they will have there passwords once they sign up to your ORG as a purchaser/member.
3. Using Mail Chimp/FusionHQ ( Third Party Getway) an E-mail list will be created where your customers e-mails will be listed automatically. So, that later you can use that mail list to create e-mail companies or sending newsletters.
4. For online shop I will setup a shopping cart on WIX by using any specific cart of your choice or best one of my choice, once you give permission.
5. Payment get way can be PayPal, which is mostly used and trusted. I will crate an PayPal gateway for you by creating a Merchant account account on PayPal or if you already have one, in that case I will setup the Pay button so that your customer can easily buy.
6. Other payment method like Skrill merchant Account or VISA, MASTERCARD, VISA DABIT etc can also be added as payment gateway.
7. Finally the Interconnection will be created between your office database and the wix so that you can know all the purchase info's.
Regards
Troy