Having the chose of only those 3, I'd probably go with the controller. It really depends on how well you solo, or how much you enjoy playing each of your toons, but the controller's pets and your debuffs look like the winning combination to me. That's not to say the others can't solo well.. I know they can.. but you're asking for an opinion, so there's my choice from those 3.
The other thing you might want to consider is their existing badges. You mention that you have been here for 5 months, but does that mean you first started 5 months before now, or that you tried it a while back and just came back for 5 months this time, or that your total subscribed time is only 5 months? The reason I ask is because there have been Anniversary badges given out to those logged in during certain time periods. Those are currently not possible to obtain, so any character that has one or more of those would be the ones to use.. if you were trying for as many as possible. This might not apply to you though, as I don't think we had any such badges since you started.
So with that information in mind.. none of your characters have any advantages over the others, so I might even suggest you start a new character altogether.. like a Tank or a Scrapper for your badge hunting instead. That might help you solo some of the harder stuff better, and will certainly help later on when possibly trying to farm for your damage badges. Those ATs have a higher Regeneration cap, so they wouldn't need an extra player/account to heal you repeatedly to make sure your farm works correctly.
As far as getting the healing badges, those can currently be done on any AT the same way, so I'm not considering that a factor. (I first got Empath at the old 1 billion requirement on my Katana/Regen Scrapper who has no heal-other-type powers. Just recently, I also got Empath on my Invul/Axe Tank as well. She has no heal-other-type powers either, and it took less than 3 days for me to earn my 400 rep for the required Gladiator, set up my Arena farm, and get all the badges while I was sleeping or at work. The 3 days also includes time I wasn't even farming.. when I was home and playing TFs or other activities.)
Just make sure that if you decide to make a new toon, that you do your best to get as many of the Halloween badges as you can right now, so you wont have to wait until next year.
I would go with the controller as well. A lot of the badges are a pain and very time consuming to do solo. I know my main is a badger (still not in the 600+ club) and when I was badging I spent long periods of time not doing anything else. I have never played a ill/ but I have played a /rad controller and I suppose an ill/rad would be good at badging. It also depends on which badges you intend to go for. If you are looking at all, all the badges, remember the Ouroborous badges can be tough. I have all the O badges on an Ice/Ice blaster and some of them on a tanker. The player debuff mishes and the no enhancements mishes are challenging, personally I would not even consider bringing a defender to those. In hindsight though the O badges were by far the most fun to attain.
Hey gang! I've come to the point now after playing a little over 5 months to where I'd like to start going after badges. Thing is, none of my friends are into it and it's going to be a solo project. Now really I have only 3 toons that I really enjoy and whom all are lvl 50 or darn close. I have a 50 emp/dark defender, a 50 kin/elec defender, and a 44 ill/rad/fire controller. not really into any of the other ATs enough to enjoy badging them out. Keeping in mind that most of this stuff aside from the TF badges I'll have to do solo, which toon do you folks this would work about best for badging out? I'd like to get as many as possible. Really have something to focus on. Again, I really like playing all three but I really want to focus on only one for the purpose of badging. Thanks for any input you can give me.