Anyone can suggest a match for you. And you can chose anyone you want to be the “go between”. However, keep in mind, that it is better with shadchanim who have the tough experience to carry it through to the end, either way it ends. THey need to have the time, and brains. Because they have to know how to present things, and come back and forth negotiating in a way that always makes you feel like either the deal is too good to turn down, or that you are making a move against your own best interest.
So once the other side says they are interested in you, you must get to work on calling anybody and everybody who knows or knew something about them. You don’t just want to call the references they have offered. YOu want to call the people that they didn’t offer. If you hear from more than 1 person something negative, that scares you, stay scared and don’t look for a life of torture.
If you hear only good things, read between the lines, like a mentalist to the “way ” they offer their information. Then pounce on the word in the sentence that sounds questionable. Weigh things. Ask others who know them.