I don't know of any books specific to that location and time (The Tudor Tailor series and Janet Arnolds Patterns of Fashion 3&4 cover the period in England in terms of construction). So, we'll take each item separately. In terms of researching the fashions, the rich and the military will be the easiest. Surviving examples of clothing in museums such as this ensemble at the Met or this one in Munich won't be overly common that far back, but paired with portraiture it can give you a good idea of the wealthy and fashionable. Artworks can be found many places from museums, to wikipedias art gallery, or even pinterest. Once you get to know a few artists names you can search from there. While there will certainly be distinct Spanish fashions, the garments will rarely be entirely unique to the area, so research the time periods garments and terms to start.

As for the lower classes, that isn't an easy thing to research that far back. Occasional prints/sketches can be found such as this German print of Spanish ladies circa 1540, but you need a working understanding of the garments you're looking at first. Interpreting art can be difficult. Check for books around that time, many still have prints and imagery in them.

When it comes to the textiles available you'll be looking for wool, silk, linen, and cotton. The basic history of each can be researched fairly easily. With trade routes well established through Europe, this is not something you need to think of as specifically Spanish unless you're researching at an extremely detailed level. For example, Spain monopolized the merino wool industry from the 12th to 16th centuries. Other wools would have been available, but this might have an effect on a person in the particular areas where that industry could be found. Or that cotton was first brought to Spain as early as the 9th century by the Moors, before it was common in the rest of Europe.

As for what was in the average persons closet, it's impossible to say. I couldn't tell you how much clothing the average person owns today, either. The most important thing for any person to have multiples of is their undergarments. Shirts and chemises should be changed very regularly (daily or more), so everyone should have a good supply of those. Outer garments it's of course preferable to have at least two or three ensembles in case something is being cleaned or fixed. As for those with wealth or the desire to be fashionable (you don't need both, but it helps) they could have dozens of garments.