Rosewater is made by traditional distillation methods, without the need for much equipment. When you distill the rose oil, the water left over (hydrosol) is the rose water. It should be relatively easy to do if you are after the water only; getting good quality oil is what is more difficult.
You can use recipes intended for cosmetics, there are no safety concerns in this case. People tend to separate essential oils for cosmetics and for food purposes for two reasons: one, industrial processing may contaminate the oils with random substances not checked for food safety, and two, essential oils tend to have toxicity on their own, and if consumed at all, are only safe in tiny amounts. The first obviously does not apply in your own kitchen, and the second is also about the oil, not about the water.
A third consideration doesn't apply to your specific case, but I am writing it nevertheless, since other people may rely on this post too. If you only have access to commercial roses sold for bouquets, they are not safe for consumption, since they are frequently treated with non-food-safe pesticides and herbicides. For rose water that is fit for consumption, only use rose petals with known provenance.
As for the variety, the traditional roses for rose oil and rose water are damascena cultivars, especially trignitipetalia. Rosa alba is the second popular choice in cosmetics, but its aroma is much subtler and doesn't do well in culinary applications, with some exceptions like tea. It is very unlikely that you will have a damascena in your garden, since they are not a popular choice for a decorative rose, and almost certainly not a trignitipetalia (it doesn't even bloom unless it can get the exact conditions it needs), although a comment mentions that they are seeing a revival. Still, if you are not the kind of person who goes to a nursery to pick the exact cultivar you want, you most likely didn't end up with an oil rose. So, the best you can do is to go by your nose, and use petals of the roses which smell strongest. You will likely have to use petals from several bushes anyway, since the distillation yield is low.
If for some reason your plan doesn't pan out, Turkish, Middle Eastern, and sometimes Indian food stores also carry good quality culinary rose water for surprisingly good prices. If you need something special (e.g. organic, or with real rose oil added), you should be able to find it online too.