What do you mean by e-signature: a certificate-based digital signature or an image of a signature/some text? Which product (Acrobat/Reader) and which versions your clients will most likely use? The answer to your question may depend on that.
I am not sure which type of signature I need. I am wanting something that is legally binding. I would assume most users would be using Reader. As for versions, that is a toss up.
Forgive me if my answers are vague, I am a little green on using this.
You probably want to use e-signature (Fill&Sign feature in Acrobat/Reader XI and DC). You'll need Acrobat Pro to create PDF form with fillable fields. But it looks like Acrobat does not allow for applying e-signatures to fillable forms. Perhaps someone more knowledgeable on this forum can answer your question.
As to placing PDF that you created on your Web site you'll have to upload this PDF to your Web site as you do with any other document.