Welcome to the forum John. The above is good advice. My wife has used three ancestry search sites in her searches; Ancestry.com, Curiousfox, and Genes reunited. Riverkilt is correct, it can be addicting. There are other benefits to searching your heritage. As a direct result of her searches, we now correspond with distant relatives in Australia, Ireland, New Zealand, and Scotland. Our younger children now enjoy conversations with their new cousins giving them different perspectives of the world.

I did a quick search of the Scottish Tartan Authority for Connelly. I found two district tartans (Dundee.) Here's the link.

http://www.tartansauthority.com/web/site/cart2.asp