Hi staefanam,
Welcome to the Mattress Forum! 
It sounds as if you are on the right track in your search, reading through the mattress shopping tutorial, but it sounds as in your current situation that you’re looking for something that you can get quite quickly shipped to your home, so the thread that you linked to with the “Simplified Choice” mattresses would be a good start. There are many items there within your price range.
As you want something that is easier to for you to reposition in while you are using it, I’d make it easy and eliminate items that use memory foam in their upper comfort layers. As you are a side/back sleeper, look for something that either offers a “plush” or “medium” option or something that has an “adequate” amount of comfort layers as to allow for your shoulder and hips to sink in a bit while sleeping upon your side.
You’re correct that there isn’t too much value in a used mattress (unless you’re hiding your money in it :cheer: ), so I understand your desire to not invest too much into this product. But if you do decide to keep your mattress, most of the mattresses you’re considering are easily transported when moving to a new destination (albeit in their “fully inflated” size, not compressed).
Looking through the simplified choice list, there are quite a few items that would on the surface objectively meet your criteria. However, only your own personal testing will be able to tell if a product meets your needs, so be sure to investigate fully any potential return/exchange policy that any company you consider offers. I would have a detailed phone conversation with any manufacturer whose mattress you’re considering to gather their advice of what product in their lineup that they feel will provide you the back chance at success.
If you desire to be even more strict with your budget, post #4 here and the posts it links to also include many of the better ever lower budget online options I’m aware of as well.
I know this is sort of a quick answer, but I sense that you have quite a few things on your plate and it sounds as if you’ve already done quite a bit of reading on the subject.
Phoenix