Jbrew, generally speaking the slower the disc, the easier it will be to control. The best thing to do when learning disc control and trying to throw straight, is start out throwing a putter, then throw some midrange discs, then the slower drivers known as fairway drivers. Discs with really wide rims like your Groove are very advanced discs that are best in the hands ofp layers throwing over 350'.
At this point you'll probably want to avoid anything that's rated faster than a Cyclone / Leopard / Gazelle.
You'll also want to look for discs weighing between 165-170 as opposed to 175 grams.
Another good tip is to research the stability ratings of a disc before you buy it, because you'll want to avoid overstable discs. For example, Innova rates their discs with a speed, glide, turn and fade rating. Speed is how fast the disc is, glide is how long it floats in the air, turn is how much it will want to turn right while it's traveling fast, and fade is how hard it wants to cut left as it loses momentum.
So for example, let's compare a Leopard and Viper.
Leopard: 6 5 -2 1
Viper: 6 4 1 5
As you can see the Viper is rated as a disc that goes HARD left at the end, while the Leopard is design to be a relatively straight flyer.
Some Innova discs I'd suggest trying out would be the Aviar Putt and Approach disc, Sharks, Leopards, Coyote and the Gazelle. If you have other brands available in your area you could look for the Buzz, Magnet, Cyclone, Magic, Element, Comet etc.