I have a new book that has the author's signature on the title page.   Is it okay to post?

Yep.  I often trade/offer signed editions.

Postable, unless the signature/autograph is on a text page. 

And title pages are not text pages.

From the Help Center under Book Condition Criteria:

Pages:

• No torn or chewed/gnawed pages
  • yes, that does say "chewed/gnawed". That means no pet-chewed (or human-chewed) books.
• No loose or missing text pages
  • for travel guide books - maps if designed to be detachable may be detached, but must be included.
• Cover not water damaged (there may be no water damage to any part of the book)
• No writing or highlighting or underlining on text pages
  • a signature or note on the flyleaf or inside front or back cover is OKAY
  • an author's signature on the title page is OKAY
  • writing or highlighting or underlining on the text pages is NOT OKAY
    • Exception: if it is a textbook or workbook, these are expected to have highlighting/underlining/writing
      • if you post a textbook/workbook, the condition must be described to the requestor in a Personal Message
      • AND the described condition MUST BE AGREED TO in a reply PM before the book is sent
      • This is the one of the ONLY three cases in which a PM exchange about a book is required before the book can be sent (the others are for travel guidebooks and cookbooks--see below).
    • Exception: if it is a travel guide (not a picture book but a guide, such as Fodor's or Lonely Planet), some writing on text pages could be expected. All maps must be present and included with the book - if detachable it is OK if they are detached, but they must not be missing.
      • if you post a travel guide that has writing in it, the condition must be described to the requestor in a Personal Message
      • AND the described condition MUST BE AGREED TO in a reply PM before the book is sent
      • This is the one of the ONLY three cases in which a PM exchange about a book is required before the book can be sent (the others are for textbooks/workbooks and cookbooks--see above and below).

• • No staining

    • Exception: Cookbooks may have some mild staining, since these are used in the kitchen and while cooking, and some minor degree of staining could be expected in a used cookbook. Also a small amount of writing in cookbooks could be expected
    • • HOWEVER, if you post a cookbook and it is stained and/or written-in, the condition must be described to the requestor in a Personal Message
    • • AND the described condition MUST BE AGREED TO in a reply PM before the book is sent
      • This is the one of the ONLY three cases in which a PM exchange about a book is required before the book can be sent (the others are for travel guidebooks and textbooks/workbooks--see above).
  • this exception applies to the covers of cookbooks also.
• Page edges: remainder marks are OK. A name written on the page edges is okay (if it does not bleed in and obscure text on the text pages)

I LOVE to receive books autographed by the author!!

Yep, I would take that as a bonus too. I've seen books listed separately here as being signed by the author, probably more as an incentive than anything else, but it's not required.