All of this ignores that the site itself, being without any of the safety features that will soon cover it, has a number of different possibilities from holes to misplaced equipment. As such it helps to take whatever steps necessary in order to ensure your own safety, and that starts with the very clothes you wear to the site.
A good place to start is any store or place where you get the best clothes, various stores can be such WorkWear Hub, where you can find all of the clothes you would ever need for workplace safety. You need to determine which risks you are most likely to encounter and dress appropriately. While there is any number of possibilities you will not think of or be ignorant of, dressing for most the dangers you are aware of will take care of most potential hazards.
Starting with the head and working your way down, it is easy to establish a checklist. The helmet is the obvious place to start. There are plenty of things that can drop on your head at any moment and so having something to enhance the protection your skull already confers is not a bad idea. The helmet needs to be thick, fit comfortably, and be certified for the work you will be doing. However, this is just the first item.
Goggles are always a good idea. Note that this is not just a pair of glasses but a serious pair of wraparound protection; it needs to not only cover the area in front of your eyes but the side areas as well. Your eyes need plenty of protection from not only splinters and dust but the odd nail or chemical spill; protecting just the area directly in front of them is hardly sufficient. Note that sunglasses are not sufficient protection against workplace hazards as they are just too thin and they do not offer full protection.
Earplugs and noise-reducing earmuffs are important for those dealing with loud equipment. You will also want a safety jacket and safety pants; the thick fabric will prevent a lot of minor injuries. A good pair of thick gloves should be on the list as well, preferably leather in order to prevent hand injuries and act as insulation. Throw in a safety vest to increase visibility and you should be doing pretty good. Debate an air filter mask; if you are dealing with chemicals or some materials they are mandatory.
Boots are a major part of every checklist and for good reason: They are well-designed to protect your toes, heel, ankle, and other foot areas from injury. A steel-toed boot will protect you from most toe injuries considering how many times you step into an area without looking at it first. They also offer some ankle support and are also usually thick enough to prevent a wide range of problems as well. Boots are just as important as the helmet and well worth the cost.
The biggest decision will be between overalls versus pants and a thick jacket; while the overalls provide better protection they are also hotter, which may not be a good idea in all areas. Keep in mind that you want to avoid piling on too many clothes; sure, coats provide thicker protection but they may also create the possibility of heat exhaustion as well as increased fatigue. Nonetheless, wear what you need to provide protection from harm and you should be safe in most situations on a construction site.