How to collect payments for a SaaS web app?

Depends on a few factors. Your home Country is one, if in the U.S. and the values are typically sized for credit cards, then use Stripe. Stripe is the easiest one to use, they are quick and things just work. Only time I've seen people complain about Stripe is when you are running a business that is in the no-no banking zone (e.g. porn etc).

I've personally used Stripe, and I've also done integrations with FirstData directly amongst some others. Stripe is easy and quick, and you can get better than 2.9% with them if your volume picks up.

If you are in the Enterprise range of pricing, e.g. 10's of thousands of dollars per client per month than you typically want to invoice and be paid via ACH/Wire.

I use https://paddle.com/ for https://www.checkbot.io/ (a Chrome extension for SEO), primarily because they act as a reseller and handle all EU tax obligations for me. Fastspring and Gumroad are other ones to consider if this is appealing.

Let me know if you've got any questions. Generally you need to list all your requirements, narrow down the payment provider that does what you want and follow their integration guides. You generally integrate your SaaS with them using web hooks.

Stripe is really nice if you have a discount code for the first xxx$. I found it really expensive without a promo code @2.9% or something around that depending on volume