The key factors are going to vary from person to person. You'll ultimately have to decide for yourself what's more important. As far as warmth goes, that's going to depend on where you are going, and how well your body handles the cold.
Just like you noticed, sleeping bags fall into one of those classic triangle patterns with the other factors you listed: Cheap, Warm, Lightweight/small size - Pick two.
In my opinion, I believe that the process of selection for a sleeping bag goes material, then warmth, then price.
Material choice is basically down vs synthetic. For a down and synthetic sleeping bag with equivalent ratings, the down bags will generally be more expensive, lighter weight, and pack smaller. If you are backpacking in places it can get below freezing, down seems to be the only suitable choice.
Generally, down is superior in all aspects except for two: it's more expensive, and if it gets wet, it's pretty much completely useless until it dries. Synthetic bags will still keep you warm if they are wet, while after frosty night in a wet down sleeping bag, you might never wake up.
Personally, I find the packed volume to be more important than the weight difference. A down sleeping bag is often smaller than it is lighter relative to a similar synthetic. I have both a synthetic and down sleeping bag. My synthetic weights 2 kg, while the down sleeping bag weighs about 1.3kg. The synthetic bag cost a hair over half as much as the down, $139 on sale vs $260. However, the synthetic bag takes up a massive 35L packed, nearly half my pack! The down bag on the other hand, I can cram into a 8 liter compression sack.
However, there are synthetic bags that can be more reasonably compressed, but then they approach the cost of the down bags.
Once you have a material choice, generally the colder you go, or the smaller you go, the more expensive it will be. You'll have to decide where the tradeoff is between size or warmth and price.
For the OP specifically I think for the 35-45 range, you should be able to find a suitable synthetic sleeping bag that doesn't occupy too much of your pack. I am heavily biased from going on many trips where getting down to 10-30F is fairly frequent.
And of course, you can also buy yourself 5-10 degrees F or so of extra warmth with a sleeping bag liner, along with the added bonus that they protect your sleeping bag from getting filthy.