You can get warm sleeping bags and you can get lightweight sleeping bags, but if you want both, you’ll have to pay-up. Do it. The sleeping bag is the most important piece of equipment, together with the backpack itself.
Sleeping bag temperature ratings are standardized according to EU norm 13537, this standard is used universally, also in USA. This means that the days where each and every sleeping bag manufacturer exaggerated the insulating effect, is over. Luckily, and finally, you can now trust and compare the temperature ratings on sleeping bags, across brands and models.
Down bags are lightweight, compressible and more breathable but also more expensive and absolutely need to be kept dry as a wet down bag is next-to-useless and could lead to hypothermia. However, the state-of-the-art down bags are now treated to make the feathers less prone to humidity absorption, hence decreasing the largest draw-back of a down bag.
Synthetic bags are cheaper and still isolates somewhat even when wet or damp, but heavier and less compressible than down.
If you can afford it, you should probably invest in a down bag, especially if you’re aiming for a thru-hiker. And consider packing it in a thin lightweight dry-back, it could save your life to have a dry sleeping bag if “shit gets real”.