D..
Well, they are safe, but they don't last long at all. It's a lot of money for not a lot of return, in my opinion.
Instead, ask about a keratin treatment that lasts between 4 and 5 months. That's a lot less product on your hair than Brazailian blowouts as often as you'd have to get them. The keratin treatment is more expensive than the Brazilian blowout, but lasts a lot longer and is a lot more cost effective. You also have to use a specific shampoo and conditioner, just to let you know. Try an Ulta with a salon if you have one in your vicinity. They train their stylists to use the product. The more experienced the stylist, the higher the price, but it's worth it. (Like the lead stylist.) Ulta is good, and less expensive than a high end salon.
The thing though that I want to mention is that when you have thin hair, it being straight accentuates that you have thin hair. Maybe that's better than frizzy hair to you though...
Oh, and it's fine to color and do keratin treatments. You just have to wait two weeks between each one.