Matrimonials sites are geared towards getting people married, not dating. So it is imperative that when you contact another individual from the site that you show yourself to be serious.
Do not say phrases like “what’s up baby?” or “what’s cooking”. You should mention why you feel there may be a match between the two of you. Tell her positive qualities of herself like what she likes to read, her favorite activities, etc..
Not only do you show yourself to be someone that reads profiles but it also looks obvious that you are serious. It also does not hurt that you are flattering your prospective mate before even meeting them.
Try to avoid writing too much. People have plenty to read and they can generally know if they are interested within a short amount of time anyways. Some people practically post their resumes when doing a first contact but it is not a good idea. The girl will know you more through conversation, not reading your resume.
You also want to leave something to talk about later. There are important things that need to be said when contacting each other but the rest can wait for you two to get to know each other. Another reason not to have a lot written in your first contact because the other person will generally not have a lot of time to read it all. Then when you find out they skipped a few things, you will feel bad about it. Maybe even get a little bit mad.