First of all the best lawyer is yourself. You will do it faster, probably better and of course cheaper. Unless you have a reason to need the help of a lawyer.
Unfortunately I think you missed the deadline for this year's 631. It should reach the cap this week, tops next week. And till you collect all the necessary documents it takes longer.
You can either try to find for arranged employment, wait for after 26th June's list in case 631 will be in it again or to look other immigration categories.