Under $200 is tough. For that kind of shooting a 3-9 is more than enough. A
Leupold VX-I comes in right at $199
The Nikon that you have already mentioned is also a good bet. I would also take a look at the
Vortex Crossfire line. Vortex makes a crossfire in
1-4x that looks very interesting, but I do not have experience with it.
If you could bump your budget up slightly, I would recommend the
CMR Leatherwood Hi Lux 1-4
And if you get the sickness and really want to do some damage, the single best optic I have ever purchased dollar for dollar is the
Vortex Viper PST 1-4x
I have the Vortex on my AR.
Why do I have such a hard on for the Viper and low magnification scopes generally? I'm glad you asked...
The Viper has an illuminated reticle that is probably the best I've ever used. It lights up in a sort of donut shape with a pin point in the middle. This sucker is fast. On my shot timer, my times are identical with a red dot sight and this scope on 1x. It is an extremely easy to see reticle against any background. But it is also capable of pin point accuracy, unlike the red dots, which cover 6 inches or more of your target at any real range. I've also used the reticle to great effect for ranging and holdovers. I've shot my rifle at balloons 500 meters away and get hits every time because the glass is clear (something cheap scopes just dont offer), my reticle is small enough that it doesn't cover the whole target, and the reticle helps me make choices. Besides all that, the Viper turrets are great and come with shims for zero stops.
Realistically with a mini 14/ar 15 shooting 223/556, the longest shot you can take is 800 yards. Usually less than that, and in your case 100 yards. You don't realistically need magnification at that distance. Lots of people can shoot irons at that distance and keep their groups sub MOA. 1-4 scopes are light, and often come with nice touches like illuminated reticles so you can go fast and be accurate.