Hi Bill,
Best of luck in an admirable undertaking! My dog is a rescue and I we will never have anything but in the future.
As for 501(c)3, in Wisconsin anyway (and I assume elsewhere), you can start by filing your articles of incorporate with the state with the intent to file your 501(c)3 with the feds. The state decision is usually faster and then allows you to operate as a 501(c)3 pending the review of your federal application. I think some law schools offer free consultation services for things like this, so you might see if you can find someone to review your completed 501(c)3 application before you submit it. You might find this site useful:
https://www.firstinspires.org/sites/...ng-a-501c3.pdf
For the website, you might look at Wix and Squarespace. Both of those are pretty user friendly.
I would also like to ask that you keep any cats you house inside or in an outdoor enclosure 100% of the time - and require that people that adopt a cat from you do the same. Cats kill an estimated 2.4 billion birds and 12 billion mammals in the US each year. Outdoor cats also transmit diseases to people and have shorter life expectancies than cats that are always kept inside.