Is it possible to process payments and keep user on the form?

As I said, I used the Payment Wizard to create a form, but now I'm locked in to PayPal with no other option. When the customer hits submit, she is taken straight to PayPal. Is there some way for customers to submit, have the order "collected" into the database, but not go to PayPal?

I'm not sure what would you like to do exactly, but with regular PayPal field your customers will be forwarded to PayPal's website. The only way to stay on the form and process the payment is to use PayPal Pro. You can check here the difference between PayPal and PayPal Pro.

But anyhow, when they submit the form it will process the payment.

Can you please give us more details how would you like to process your payments so we can give you the best possible solution?

Thank you!

Thanks for your response and follow-up question. I would like our customers to have an option of paying COD (i.e., check or cash on delivery). In other words, if they don't want to pay via PayPal, I would like them to be able to "submit" a payment that I could then process for delivery, and then collect payment upon delivery.

Thank you for clarifying your problem. 

What you can consider using in this situation is Purchase order form, where you can create all your products with prices etc.

Then your customers will submit the form with their information plus list of products they would like to buy:

And you can deliver to them when they can pay for a product.

Hope this could help, do let us know if you need any further assistance.

Thank you!