Hi Aaron,
I have done extensive research and testing to find the best Twitter tool and I prefer SocialBro (www.SocialBro.com). You can filter by all of the criteria you mentioned as well by influence, by how often a user is listed, by account age, by time zone, country, gender, etc. It also allows you to monitor tweets, find the best time to Tweet, create lists and analyze competitors.
I do have an affiliate link for SocialBro; however, I am not recommending it for that reason. It does all that you need and it has a free trial so you can try before you buy. If you would like to use my affiliate link, it is http://get.socialbro.com/fB7v.
Thanks,
Christine DeGraff