That's actually a good question, but I don't think I have a definitive answer for you.
I used to use 3/4" and 5/8" wood when I was starting out (I used to buy cabinet doors from HabitatForHumanity ReStore, that had, you guessed it, 3/4" and 5/8" hardwood panels). Then I started buying rough cut (4/4) lumber and would plane down one surface flat, and usually end up in the .85"-.93" range. One HUGE investment that has paid off for me, particularly since I have been using more and more expensive woods, is a bandsaw with a generous re-saw capacity. I bought the Laguna 14/12 (14" bandsaw with 12" re-saw capacity) which has saved me a lot of money/time/wood. If I have a model that is going to be smallish (under 8" tall), I used to lose a lot of wood because I would remove it from either the top or bottom (with CNC on roughing pass, or sanding the bottom). But once I got the bandsaw, I could cut my wood to suit the size/depth.
All that said, you have to really trust the render/simulation in Aspire. One of the downsides of leaving some wood on the bottom of the model is that Aspire won't cut through the wood if you don't tell it to, so unless you get rid of the scrap wood (in the render) it's hard to judge the finished height of the model. 2 ways to overcome that (if you can't/don't create a profile path) is to use the 2-sided modeling in Aspire, and create a fake pocket cut on the back to remove that extra wood (in the simulation) and the other is to create a fake profile toolpath and cut out the piece with that (you can create ridiculously small virtual-bits that basically laser engrave the piece out (in the simulation) so you can remove the scrap once the toolpaths have been created (by double clicking on the scrap wood in the simulation.
One "trick" that I have learned that is if you have a relatively thin model, and want to give it some heft, is to add on some material on the bottom of the model by increasing the base height in the component properties tab. I wish there was a way to select zones that you want to increase/decrease the height of only that particular zone (imagine dividing a model into layers in thirds, and raise the top a certain amount, keep the middle the same depth, and reduce the bottom). In 3D modeling there is something called "soft selection" that allows for this type of thing.
Anyway, I never answered your question, but explained how to deal with removing extra wood, or add heft to a model. I think a lot of it will come down to what looks/feels right. Sometimes you have to just cut it and see if it looks good, and keep a log of what works for you. Be prepared to make a lot of expensive firewood though