In reply to frankboase:
As luck would have it, I'm in the process of planning a HRP section hike (starting mid next month).
I recommend the Joosten book, published by Cicerone. Apparently the book has its quirks and is not 100% accurate, but I've found it very helpful for planning. The trekking season in the Pyrenees is, broadly, July to September – outside those months snow appears to be a much bigger issue.
Your main expense is likely to be travel from the Philippines. Once actually on the HRP it seems possible to live very frugally if you want to, although if you stay and eat in refuges all the time then costs will add up. Wild camping is the cheap way to do it!