Hi drm80,
The first place to start your research is the mattress shopping tutorial here which has all the basic information, steps, and guidelines that can help you make the best possible choices … and know how and why to avoid the worst ones.
No this isn’t accurate at all and there is no specific minimum thickness that would apply to any specific person because it would depend entirely on the specific materials and components that were inside the mattress much more than just the thickness of a mattress and thickness is only one of many factors that can affect whether a mattress is suitable for you. Some mattresses that are thicker may be completely unsuitable for you to sleep on and others that are thinner may be a great match for you in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences) depending on the specifics of the mattress although in very general terms people that are in higher weight ranges will often tend to do better with a thicker mattress than those that are in lower weight ranges. There is more about the effect of thickness in post #14 here.
In addition to the tutorial … post #3 here and the posts it links to also have more information and guidelines that will be helpful for those that are in higher weight ranges to make the most suitable and most durable possible choice.
Some of the better lower budget online options I’m aware of (subject to the guidelines here) are listed in post #4 here and in posts #3 and #4 here although I would tend to lean towards the higher end of your budget so that you have more options available to choose higher quality and more durable materials.
The better options and possibilities I’m aware of in and around the Indianapolis area (subject to the same “value” guidelines) are listed in post #2 here.
Phoenix