I think it really depends on what the person is looking for.
The vast majority of people who want a relationship usually have a certain character in their minds, a certain life story, and they are looking for the person who will fit that (and will want to fit that, for the matter).
In that case, is the beginning of the story that important for you? Does it have to come about through romantic serendipity (the main "theme" these days, due to movies and books)? Does it have to be related to being with friends, meeting her in the same circles you go with them? Does she have to be introduced by your parents, who first did the search among their friends daughters? If the "introduction" of your story is really not important, then marriage arranged by third-parties may be an option.
The first thing you have to remember is that it's logical to expect a lot of vultures parasiting human need of love in that. Never researched that, but I would expect most of what exists to be scams to get people's money and green cards. I would have to do research to find out which companies are really into matchmaking and which have confirmed good reputation - trusting not the "cases of success" (which may well be just biases propaganda) but assessment by third parties.
But before all that, think about your responsibility. If you find a trustable matchmaking site, if you find a nice girl there, she will be full of dreams for her life with you. I suppose you are in the US or some 1st world country right? She will have all those movies images with nice two store houses and two cars, green yards in her mind. Even if she has an "average" situation in her country, she expects the "average" situation in the 1st world to be significantly better. What I'm trying to say is that, even if she is not a social-climber, you still will be responsible for her well-being, both financial and psychological, much more than in a usual relationship where if the girls wants to quit, she simply gets her things and go back home.
Always remember she will be the one saying the poem below to you all the time, even if she never read it.
"Aedh Wishes for the Cloths of Heaven" William Butler Yeats
Had I the heavens’ embroidered cloths,
Enwrought with golden and silver light,
The blue and the dim and the dark cloths
Of night and light and the half light,
I would spread the cloths under your feet:
But I, being poor, have only my dreams;
I have spread my dreams under your feet;
Tread softly because you tread on my dreams.