Including your company name and website in the footer is a totally normal and common practice.
I think whether it's okay or not depends on the expectations you set in the beginning.
If you show your client a version of their website without your company name in the footer over and over again for 6 months and then when you go live you slap it on there, I can imagine the client being unpleasantly surprised that you did that, and I'd say justifiably so.
But if you somehow communicate to the client at the very beginning of the project that every website you do includes certain things, and one of those certain things is a link to your site, then that of course eliminates the possibility of surprise later.
I often offer my clients a "Chevy version", "Pontiac version" and "Cadillac version" of a project/feature/website I might build for them. I would recommend to you that you do this in general. Your Chevy version could include your advertisement and your Cadillac version could exclude it. (Offering multiple packages is a good idea anyway because it changes the question from should we proceed to how should we proceed, and it lets the client feel like they're in more control than if you offer a single take-it-or-leave-it package.)
So to answer your questions:
- Is it amateuristic? If you sneak the link in hoping no one will notice, that's super amateuristic. If you include the link as part of a certain package and communicate the fact up front, then that's totally professional. Whether it's amateuristic depends not on whether you do it, but how you do it.
- Is it bad for SEO? I'm not an SEO expert but I have a hard time thinking of how it might be bad for your SEO or the client's. I would bet money that it would be good for your SEO and have a negligible effect on your client's.
- Should you offer a "branding removal" option? Yes, but I would position it by default as a line item in a package rather than a standalone option.