Sadly, these things (traffic, aircraft) are the bane of the nature recordist's life! I don't want to discourage you, but I think you are being very optimistic if you hope that a shotgun mic will help you much.
Having said that, a shotgun mic will help you to isolate specific sounds from the general ambient background, but it won't eliminate specific aircraft/ traffic noise, just reduce it slightly, perhaps... The problem is that, although these unwanted sounds originate from a particular direction, they then reflect off any hard surface they encounter - the ground, trees, sides of the valley, etc and end up coming back at you from all directions! No mic, not even the most tightly defined parabolic reflector will completely eliminate this. At best you'll get a reduction in the unwanted sound, but also a rather skewed frequency response. (Listen to some of the bird sounds on xeno-canto.org for an example of what you can expect). So, if you want to record specific animal sounds for identification purposes or study, this might be ok, but you won't get a "pleasing" or "immersive" recording this way. Also, with just the one mic it will be single channel, mono.
Although this might sound counter-intuitive, many nature recordists use omni mics in various configurations (spaced or baffled, etc.) These give a very expansive sound and need not be expensive, but the trick is to find a quiet spot at a quiet time of day. That really is the only way.
So what I would suggest, if you're serious about the nature recording thing, is to spend some of your budget on a trip away for a day or two. Aircraft don't fly 24/7 (not quite), nor is the traffic constant throughout the day. You might get lucky locally or you might have to drive a couple of hundred miles and camp overnight, but that's all part of the game. We live in a noisy world, and *the* biggest challenge for nature recordists is to find the quiet spots. I do a lot of this kind of thing and I spend far more time looking at maps, satellite photos and aircraft flight charts than I do out in the field! Check out the work of Gordon Hempton & Lang Elliott for both inspiration & examples of what it takes.
Finally, just to answer your specific question about shotgun mics. The lowest cost mic suitable would probably be the sennheiser ME66 (or ME67)+K6. This is a low noise mic with a reasonable off-axis response, and is often used by bird recordists to hone in on single species. But that's already double your budget and, as i said above, I don't think it will give you what you want.
Good luck!
Martin