In my opinion (and just my opinion) thickness or thinness(?) means nothing. I like to fondle my fabric before purchasing -- thickness or stiffness is generally nothing but sizing.
Of course everyone should buy what they can afford, but if I were attempting to make a Baltimore Album, believe me -- I would use nothing but top quality fabric. You should be confident that your hard work will last for at least 100 years -- not fade or fall apart. With needle-turn applique, you'll want the higher thread count.
Just my opinion.