I am pretty sure listmailpro can probably do what you want, I am just not sure what you mean by sequential emails. Describe for me what your referring to and I can tell you how to go about it.

Double opt-in is going to have a much higher deliver success rate for a couple of reasons. First, some of the emails you send are going to get blocked by the recipients inbox, however, if they can receive the validation email then likely that inbox is not blocking your messages.

Second, if they take the time to validate their email account they are going to be real prospects who want what you are sending them verses people who just submit their email thinking at that moment they want to be part of your list, but then forget about it. These people, because they forgot they opted-in, may also report your for spam later on.

The downside to double opt-in is that you will get people who submit their email and never take the time to validate or get the validation blocked, so your list will be smaller.