Ok... You guys are going kinda nuts... I just asked a simple question. I don't care about the JRing being gone. I've had it for 3 years and it's served it's purpose. What I was looking for was an idea for a good first weapon that if stolen wouldn't hurt me to much. I'm not buying an eraser or a TRing. If I were to buy anything it would be a Moehog Skull.
we got a little philosophical, it happens sometimes and subjects get far afield
If you always use your freezer on the first round, it should go in your first slot. If your opponent tries to steal it at the same time as you use it, they won't get
anything 
The main problem was working out whether or not you could get the JBR off first. Without that, the answer would be obvious.
Taking out the JBR from the equation, I'd say a reflector personally. I carry a reflector in my first slot since it's the only weapon I can do without if stolen. Though it could be used against me very effectively, I can rely on my backups to get around it. In fact, in the event it is stolen there's a roughly 75% chance that my opponent will it. You can essentially turn that weakness into an advantage by using your opponent's temporary boost in confidence against them.
Going on what Piano suggested, a freezer is a good choice since most of the time you will use it first round. However, that aversion is dependent on whether or not your opponent steals on the first round. That part is not guaranteed. If that's the case, a secondary defender would be next in line (such as a PCH if you have a Gshield/FTab already). You could also stick a junk weapon in there as well.
For the most part you never want to give your opponent an offensive weapon unless it's
completely useless. That should hopefully narrow down the search.
It's workable if you let your friend have the Eraser starting off.
A. TRing - Eraser
B. JBR - Bomb - TRing
User (A) steals JBR.
A. TRing - Eraser - JBR
B. Bomb - TRing
User (B) steals TRing and Eraser. JBR is in first slot. Eraser in opponent possession.
A. JBR
B. Bomb - TRing - Tring - Eraser
Now, this is where it gets tricky. Since the JBR is not in the possession of its original owner and gets erased, the question is will it return after the battle or is it gone? You could use the stealing and return of one-use/fragile as a reference but since the Eraser's effect is to permanently delete, I'd think it would change in this scenario.
It would work the other way with both Eraser and JBR in the original owner's possession if the stolen items appear in front of the TRing instead of behind it in order. That one I'm not sure, though it's likely they show up following the Ring.