If you are looking for something free or low cost, then you can go to one of the organization. But if your case is a little more complicated than the usual (if it includes deportation warrants, illegal overstay, felony), an immigration lawyer is better but since immigration law is one of the most difficult branches of law, it will cost you money. Do not go to an organization if your case is complicated. As for going faster, I am not really sure. One thing I do know, filling the papers with someone who’s inexperienced can cause a great delay, but with a lawyer who knows what he’s doing, then you do have a great shot of having everything file properly.
To be frank, immigration itself is more likely to recommend a lawyer.