You don't state a preference for active vs passive 3D. Perhaps you should read a few threads on the subject to help you decide. Anyway, I'd suggest passive. The glasses don't need charging and RealD glasses from the theater will work. I own an LG 65" passive and the 3D is very good with no crosstalk. I have a couple dozen 3D Blu-Rays now, but obviously I don't watch them all the time, so just consider that the vast bulk of your viewing will be 2D. Forget cable 3D, it stinks. That said, a 3D Blu-Ray is a nice treat occasionally. You'd need a 3D Blu-Ray standalone player.
If you go passive, you're looking at Vizio in the size you want for under $2,000 bucks. The latest 70" Sony 120 Hz passive 3D model is a little over your budget, as is the Vizio 70" 3D 240 Hz model. Sharp uses active, and while it has a nice picture for the money (I have a non-3D Sharp 70"), it's likely Vizio is using the same panel for its 70" TV. Some will tell you to steer away from Vizio, but their reliability is comparable to the other makers. The Vizio 65" panel likely is still sourced from LG.
I'm not going to recommend LG because my panel developed a tab bond problem (vertical line). I reported it just at the end of warranty, but they jerked me around so much I decided to try to fix it myself. Which I did, successfully. I think Vizio's build quality is just as good anyway, without paying a premium to LG. Anyway, when I bought it, it was one of the very first passive 3D TVs. Out of your budget anyway.
I wouldn't hesitate to go with either the 65" or 70" Vizio. Personally, I'd go 70". I can tell you my 70" vs my 65" is a worthwhile step up in size. You may not think so, but there you are. Also, I wouldn't let 240 Hz be a deal breaker. To me, the advantage is marginal, but others will disagree.
In your budget:
Non 3D Vizio 70":
Good luck whatever you get.