Cher - I am always careful about the quality of fabrics I generally use as poor quality may save on expense but may not give a good or lasting result. I consider the end use of the project. Does it need to withstand frequent washing, do you wish it to be handed on to the next generation or will you be putting hours and hours of work into it. If any of the above applies - use better quality fabric. On the other hand if you are making a project that is not expected to have a long life then perhaps the cheaper fabric will suffice.
If you already have thin quality fabric then I think starch, starch and more starch before you use it and make sure you square your blocks up after sewing and starch them again before joining together.
Regarding the PH blocks you could do "scrappy" and tie it in with one co-ordinating colour by buying different fat quarters which would add to your stash range. But I suppose I always think in FQ's as the cost of fabric here averages $A26 per metre so my stash is only fat quarters and I rarely buy in yardage.
I love Asian fabrics - would the ones you have be suitable for PH or would you prefer something else?