I have probably 7 bags I have collected over the years. By far my best sleep in any weather is my Nemo Disco. But like other have said it’s a package. I use Nemo pad and inflatable pillow. But the one thing that works best in every bag for cold weather is a silk bag liner. I use the Sea to Summit and it’s worth every penny..
I have an older synthetic fill 15 degree marmot bag that was a little over $100. I think you would be fine with a marmot Trestles bag in 15 or 0 and it fits your price range. The 15 degree bag weights 3 lb 6 oz.