I use Covert's Spec Ops Code Black. With any of the cellular game cams, you need a decent cellular (GSM....ATT or TMobile) signal, usually stated at 3 bars or better. You can get booster antennas for them if you don't have good cellular signal and depending who you talk to, either they work well or are pretty useless. I don't use the boosters and can't say.
The one I use allows for some minor changes to setting via texting, but not as much as some of the other brands (that are usually more expensive). I have my images sent to email so that I can view them readily on the home computer, but you can have it set up to just send the text messages to your phone number.
I run Eneloop rechargeable batteries (mostly) in my cams and get about 1200 images on a good run, which is common. Depending on activity, that can run me 3-6 weeks, but as much as about 8. If you have the camera watching a trail that isn't often used, maybe you get dozens of weeks out of a single set of batteries. If you are watching a feeder hit by coons, deer, hogs, turkeys, and squirrels, every day, then maybe 3 weeks. Really cold and really hot weather can affect battery life, so you may or may not want to go with a solar setup. I don't have that. I have my cameras set to take pictures as fast as possible which is a 1 minute cycle that in reality is about a 2 minute cycle most of the time, the delay being the amount of time that it takes to upload the image.
I would avoid buying anything that requires a service policy, because then you are getting hit twice with costs. You still have to pay for the phone service and then you pay for the service policy (e.g., Moultrie has this). There are some advantages to the service policy route, but I do not believe they are worth the expense.
Frank mentioned cams that won't work in the near future. 2G is being phased out and so you want a camera that is 3 or 4G capable. New models should say that they are so that you know, regardless of the brand you get.
There are new versions coming out with some regularity. Places like
http://www.trailcampro.com/trailcamerareviews.aspx and
http://www.chasingame.com/ can be very helpful. Both places have folks that put cameras through various tests, review features, etc. At least this can help you narrow down your field of choices to units that better fit your parameters.