What i did in p4 to get HQ items as a gsm, was with quest/bought gear till lvl 12, and the jewelry made by me, what I noticed that was helpful was getting the most of CP posible, IIRC I had around 195CP, so I started out with the steady hand, then depending on the lvl of durability in the item, i would either get 3 basic touch (40 durability) or 5 ones, then use master hand or manipulation (at lvl 15), with that amount of CP i was able to do 2 more basic touch or 1 basic and 1 standard touch and had enought durability to make the item with synthesis

Depending on the lvl of the item, would be after master hand another steady hand, and work with 1 basic touch and the rest on synthesis, that method depending on the lvl of the item, and luck of getting good or excelent condition, would get me 20+ % in getting a HQ item, and like Kamina said, if you use HQ materials, you normaly start around 20ish %, with my rotation I managed to make all my lvl 12-15 jewelry for my GLD and CNJ