I have a few trenchcoats in my closet, but none of them are true Burberry-type ones. For under 300, you won't get the proper material that is truly windproof/water-resistant; instead, you'll get either polyester or a cotton-nylon blend which doesn't breathe as well.
With that said, here's what I've bought over the past 3 years:
- Club Monaco navy trench (nylon) - $59 (a one-off clearance special that was just a bit too big off the rack), but I spent another 30 bucks in getting it altered to fit my frame
- Banana Republic beige trench (polyester) - $120
- Zara cotton trench (cotton) - $79
If you're adamant about staying under 300, I would try the above-mentioned places, as well as H&M. I've seen trenchcoats at H&M for ridiculous prices (<$150), but they'll feel like plastic when you put them on. Sadly, these days, you have to pay for quality.