I think a lot of benefit comes from preparation. Defining lines and standards clearly for what you refuse to accept, what you may need from another and what you are able to give.
This would be deeper than more superficial things and preferences. Then once you define them, stick to them. I have had clear lines drawn in the past and allowed myself to make excuses for ignoring them. It has never paid off.
Once you know what you need, what you have to offer and what you refuse to accept you eliminate a lot of choices before they ever show up. This makes it easier to pass up on people not good for you.
Just ensure that these are the vital issues.
Lesser issues aren't important and can change.
I have always had a preference for white women, and I'm also white. It was never that others weren't good enough or an6 such thing. I simply did not want to fuss with drastic cultural differences. Areas like that are difficult for me to adapt to.
Yet it wasn't a vital issue. And now I am dating an amazing, beautiful American born Puerto Rican woman. I never thought that would happen, but it has.
So be lenient on smaller things and know where you stand on important issues.
This also makes it easier for God to bring someone to you, if He chooses to. You have less clutter to distract or confuse you, yet still remain open.
I'd say, as far as prayer goes, a more important prayer is asking God to help you grow into the right kind of person that can fulfill their role as a spouse in a godly manner. Shining the light on what you need to do is more effective than asking for what you want. What's the point of meeting someone amazing then blowing it because you aren't ready?