It really depends on what she says.  If you are lucky enough to receive a thoughtful message that relates to something you've said or mentions a detail from your photos, you are good to go.  Pick up on the topic she started and reply to it, then maybe start another thread with her.  But all to often the messages I receive are just "Hi there".  Which leaves you zero insight into their intentions or thoughts.  In that case, if I am interested, I will thank her for messaging me.  The I'll compliment her lovely photos and thoughtfully written profile (if that's appropriate).  I'll ask or comment about something in her profile.  And if it's obvious that she has not read my profile I'll say please read my profile and lmk if you agree we might be a great match.  The whole idea is to get some sort of a conversation going.  

We don't really know what random individuals are going to prioritize.  So there isn't really a "best" response.  
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Part of the competition is getting in first because eventually she's going to shut down the firehose of responses.  The second part is standing out in the crowd.  
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I would suggest writing up an intro and then copy-paste that to all chicks in order to save time.  
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Just remember that getting ignored most of the time is just how it works.  It's a numbers game.  There are a lot of thirsty guys out there flooding her inbox.  

I'd suggest reading her profile carefully (don't just look at the pics). If there's nothing in the text, it is 90% scam.
You can respond to the pics by saying 'You look great in red' or 'cute dog' but also look for something about their work or hobbies. 'I like to ski too' or 'I'm big on sushi also' can get things going. Try to ask a question like where they would like to go for dinner. If you're stuck you can always say something vague like 'I got a good vibe from your profile and think we would get along.'
If it's pure sex you want without any kind of relationship, there are a few of those, but you need to filter to find those.
Also.. if you are waiting for them to seesage you.. my experience has been you need to go after the ones you want, and those who reach out are lower on the scale or scammers.

I believe that I have, at one time or another, done all of the things suggested.  Particularly, trying to engage them on content from their profile or comments from their messages.  That said, I also believe that I'm a somewhat unconventional SD.  Meeting with a POT weekly or traveling with them (which seems to be a common ask) is just not an option for me.  And, I say as much in my profile.

 
Maybe more than anything, I need to practice being patient and play the numbers.

 
Thanks for replying to my post.  It's always helpful.

The art of messaging is the art of conversation.  

 
What would you say to her if she was standing in front of you and just said whatever was in the message?  

How would you reply?  

Write that down, but don't hit SEND just yet.  

 
Take a minute to re-read her message?  
- Did she ask you any questions and did your reply address them?  
- Did she mention some detail from your (or her) profile and did you acknowledge it?  
- Did she leave an opening for you to ask a new question or comment on something from her profile?  

 
Now, make a few edits to your reply. Be sure to mirror her style:
- If she is brief, be brief
- If she is thoughtful, be thoughtful
- If she is vague, be somewhat vague
- If she seems to expect next steps, suggest next steps.  

NOTE: All of this must stay within the site comms guidelines. If she asks how much, be careful not to suggest any pay-for-play activity.  

 
Life is good

 
The Cat