I used Allegiant for the first time in January and was quite happy with them.
The benefits and drawbacks have pretty much been covered but I'll throw my two cents in anyway.
The major benefit is lower fares (at least for us as the other cheaper airlines do not come anywhere near my town), but I also thought the seats were nice and comfortable and the flight crew very friendly. Also, the fact that they fly in and out of smaller airports is, to me, a benefit. I, personally, get intimidated by large airports! Another benefit for me (maybe not so much for others) is that I can take Allegiant and have it be a direct flight; other carriers would require a minimum of two layovers.
Yes, Allegiant tries to nickle and dime you. I definitely agree that the "convenience fee" for booking online is a crock. However, you really don't have to pay for seat selection, or priority boarding. We paid for neither and our party of 6 was all able to sit together and we had plenty of room for our carry-ons. Yes, you do run the risk of the flight being cancelled and not being able to fly out until the next day. From what I can tell, weather concerns would be the major cause of that. In your case, yes, having your flight cancelled would be a major headache.
Would I recommend Allegiant? In most cases, yes I would. For you? I guess it would depend on your comfort level that your flight would not be cancelled or rescheduled.