For your $38 a day you get 1 CS meal - which will be worth $12 to $18 - and a snack - worth $2 - $3. So to get your "money's worth" out of the TS meal, you need to spend $17 to $24 on your meal including tax, not including tips. This is pretty much any TS restaurant in WDW. To get the most perceived value, I would recommend avoiding breakfasts, as they would typically be less money. Most lunchs and dinners will run you $25 - $35 per person. For character meals, dinners are the most expensive, though the menus are usually simialar to the lunches, so your sort of getting more value there. Check out menu prices at WDWinfo.com.
If you want to eat at TS restauarants, the dining plan is a no brainer, though it was even better when tip and appetizer was included. The only way to spend <$38 per person per day on food is to NOT eat at TS restaurants.
To give you an idea, DW and I went together 1st time in 1997. We budgeted $75 a day for food, only ate at 2 TS restaurants the whole week on property (a few off property like Chevey's), and still couldn't spend below our budget. In 2000 (eight years ago) we budgeted $100 a day for food, and again only eating at a couple of TS restaurants on property, barely managed to squeak by. In 2006 we used DDP for $76, and had more food than we could eat most days. (Note: in all 3 case, we brought our own breakfasts and ate in our room before going to the parks.) I tried to keep track, but I figured we were getting between $50-$60 of food per person per day.
The really nice thing, I think, about the DDP for the budget concious person is, when you go up to the counter to order a meal, you don't have to worry about "Oh, the chicken meal is $13, if I just get the chicken sandwhich its only $10, and we can just split a soda, that'll save us $2." you just walk up and order what you want and don't worrry about it. I suppose you could have the opposite affect, which is "What's the most expensive thing I can order" but I never think of that.
SkierPete