Hi LowSkyOrbit,
The first place to start your research is the mattress shopping tutorial here which has all the basic informtion, steps, and guidelines that can help you make the best possible choices … and know how and why to avoid the worst ones.
The type of mattress or materials in a mattress you choose is always a personal preference rather than a “better/worse” choice.
Outside of the “regular” information in the tutorial that would apply to everyone … there is some information in post #3 here and the posts it links to that will be helpful for those that are in higher weight ranges where firmer materials and more durable materials will generally be more important.
The Tuft & Needle certainly uses higher quality and more durable materials than the Posturepedic you are currently sleeping on. There is more about some of the “one choice fits all” style of mattresses such as Tuft & Needle in post #3 here and there is also more information about them that would be relevant for higher weight ranges in post #3 here.
This is really too broad a question to be able to answer because I don’t know anything about the types of materials or mattresses you tend to prefer and depending on your preferences or whether you are considering local or online mattresses there are dozens of manufacturers that may also be worth considering on a “mattress by mattress” basis (depending on the quality of the materials in a specific mattress you are considering). Only you can feel what you feel on a mattress and there are too many unknowns, variables, and personal preferences involved for anyone to be able to make specific recommendations or suggest a specific mattress or combination of layers or materials based on specs (either yours or a mattress), health conditions, individual circumstances, or “theory at a distance” (see mattress firmness/comfort levels in post #2 here). I can certainly help you narrow down your options by avoiding the worst ones and with “how” to choose or act as a fact check but not with which specific mattress, company, or manufacturer to choose.
Outside of PPP (Posture and alignment, Pressure relief, and Personal preferences) … a mattress is only as good as its construction and the quality and durability of the materials inside it regardless of the name of the manufacturer on the label so I would focus more on the materials in a mattress than on the name of the manufacturer that makes it.
There is also more about the most important parts of the value of a mattress purchase in post #13 here that can help you make more meaningful comparisons between mattresses.
If you let me know your city or zip code I’d be happy to let you know about the better options or possibilities I’m aware of in your area.
If you are also considering online choices then the tutorial post also includes two links to lists of the better online options I’m aware of as well (in the optional online step).
Phoenix