Acrobat (Pro) is absolutely the correct tool to accomplish this. However, keep in mind that the current version is Acrobat XI, which is overall much better than X (IMHO).
You will work in the Forms Edit mode (Tools pane --> Forms --> Edit). There you select the Digital Signature Field tool, and place the field wherever it is needed. With the Text field tool, you place the other fields, and in their respective Properties dialog, you can set them read-only, and/or add default values, and/or add logic.
Hope this can help.