Ask your vendor to cut/drill the hole.

Go into a home center and look at the ones on the shelf or rack. You should be able to find one in your budget, there.

Are you sure it's stainless?

Why a step drill?

I'd probably use one of these.

https://www.harborfreight.com/1-18-in-carbide-tipped-hole-cutter-57963.html

Not recommending this brand, although it will probably work as good as any.

Here's one that should work. It says it can cut thru stainless steel.

Step drill bit for stainless steel

Did you forget to include the link?

no I did not, the text is clickable.

I drilled pilot holes with my hammer drill and a regular 5/8" bit yesterday. Now I just need a larger bit to make the hole 1 1/8." I think I'll try the one that PFF recommended. Thanks to everyone for your help.

" I think I'll try the one that PFF recommended. "

The problem with using a hole cutting saw now is you already drilled a hole. The hole saws use a mandrel with a regular drill bit in the center for a pilot and centering/guide hole. Hole saws do work well when there is a hole already there and you are essentially hogging it out larger. You will most likely get tossed around trying to use a hole saw now.