Frames Per Second issue

The R7 260x falls into that category as suggested by crunchipop.

You might be able to find a deal on a 270 (x) and hit that $150 price point.

The R7 265 fits right inbetween those two.

This website might help:

http://kotaku.com/battle-of-the-150-video-cards-geforce-gtx-750-ti-vs-1525383934

(At the bottom of the article it shows benchmarks for Battlefield4, it uses the same engine as this game so it's a good comparison, this game will pull more frames than BF4)

I think you'd be better with the AMDs cards over the 750Ti especially if your main game is PvZ.  Mantle should push it over the 750Ti on DirectX.

This is an interesting article about Mantle and how it acts with lower-end CPUs.

http://wccftech.com/battlefield-4-benchmarked-gtx-780-ti-d3d-r9-290x-mantle-api/

(take it with a grain of salt though, they are using monster GPUs compared to what you'd be getting)

You can't go wrong with any of those cards though, especially if you aren't a big gamer and plan to mainly just play this one.  I would guess in about 3 years they will start to show their age on the newest most demanding games at that time.

* As those benchmarks show, you aren't going to want to play current {demanding} games with the graphics completely cranked up to Ultra.  How I do it is find where the system runs steady at 60fps (or 120 for 120hz monitor), then I lower everything by one notch.  No Stutter > silly graphics.

**edit ...just this was interesting i suppose

http://cpuboss.com/cpus/Intel-Core-i3-2130-vs-AMD-A10-7850K