Here are a few things to consider as you are shopping:
The velcro I use is soft and flexible. For headbands on teeny babies, a clip is just too heavy and clunky, but velcro is soft, light and less bulky. Velcro flowers and bows are the most economical choice at Simply Lulu Boutique. Velcro bows/flowers can be used as your child outgrows her headbands, with either an alligator or french clip adapter.
Snap clips are the tear-drop shaped clips that snap shut when you bend them. I partially cover them in ribbon for a finished look and to create a tighter grip on the hair. Snap clips work great for all ages, as long as there is some hair to clip on to. They take slightly more time to put on, as you have to bend them shut. Snap clips have a super low-profile, and since they are very light, they are quite comfortable and well-tolerated.
Alligator clips are sometimes called "pinch clips." I use a ribbon-covered single prong clip, because it is easier to slip through the hair, and I attach a REALLY good no-slip grip that holds those wispy hairs. They are definitely my most popular clip. Alligator clips are more versatile because they can be used on other brands/styles of headbands, from infants to adults.
French clips are great for older girls with thicker hair, not toddlers or infants. I cover the clip with ribbon for a finished look. My french clips are a medium size, and would work great to hold back a half-up style, or adorn a pony-tail.
Any way you choose, I know you will be happy with your Simply Lulu accessories!
Feel free to contact me if you need further advice/help with your purchase.