I haven't built a lot of acoustic guitars but people have been very impressed by the sound of the ones I have. I am a hobbyist so am on a budget. I have resawn all my back and side sets from rough sawn lumber except one of my current builds of an EIR set that was left in my basement 40 years ago.
I do not do anything like tuning sound surfaces, yet. I am very happy wiith my tone and volume so far. I do not know about damping woods. I thin backs and sides to typical dimensions and use the wobble test on tops. I have used A grade tops or less to date, typically $20 or less.
In a way, I am in the "practice" mode like you are thinking of. I do not build with the intention of selling but have.
As far as economical woods go, Sapele, Black Walnut and Cherry are readily available , quarter sawn, in good wood stores with black walnut typically the highest price of those 3. African mahogany is cheaper but not usually marketed as quarters sawn. Padauk is also economical. In Canada, all these woods are typically less than $10 per board foot, except the walnut. A 5 ft. X 8" x 1.5" = 5 board ft. and will yield 3 back side sets plus 1 or 2 neck blanks and some extra bits for end blocks, etc. So $50 gets you a lot of "practice" building.
The black walnut is probably the easiest to work and bend, to my ear sounds better than maple and may be the best looking. The cherry may be the easiest to finish as it is closed grain.
I did purchase some Osage Orange very economically locally and built my best sounding guitar
https://www.flickr.com/photos/194462...77720296630125 with it but other posters are correct when they tell you it is not easy to work with, I may not use it again.
If we are discussing builds to gain experience, I suggest you go easy on the ornamentation, simple inlay, rosettes, binding and purfling. Trying to build a "pre war" or other replica can chase you down an expensive rabbit hole finding the exact materials rather than what is readily available. I recently ordered a pre war style back strip at $30 with shipping from Australia for example.
Another suggestion is to build smaller instruments, flat top mandolins, ukuleles or smaller than dreadnought guitars. 5 or 7 inch wide wood is easier to find than 8" and parlor size tops are often less money or better quality for the same. You will learn the same skills and do less sanding.
Titebond Original all the way ++
Sorry for the long winded post, Good luck with your journey.