That exactly right, you need a vacuum pump to pull all the air out of the system before you add refrigerant. If it can hold the vacuum for 15-30 minutes then there are no leaks. When you pull the vacuum, it may drop a little, thats possibly OK, just vacuum it down again. If there is moisture, it will sometimes start to boil off, causing the pressure to rise like a leak would, so vacuuming it again will remove any residual moisture.
If it were me, and I knew nothing about AC repair, considering the cost of the tools, and the amount of expereince you need to have, I would let a pro handle the refill portion. You already did the expensive part, now all you need is an evac and recharge.
There are some terminology problems, to prevent confusion I will attempt to clear them up. One, coolant is an antifreeze and water mixture to keep the engine cool. The correct term is refrigerant. If you were to go a a shop and say you were low on coolant they would top of your radiator, not fix your AC. The other terminology is a common problem. People refer to all refrigerant as Freon, which is a trademark name for R-12, which was used in most AC systems up till the early 90s. I was officially discontinued in vehicles in '94 but most automakers had voluntarily switched over a few years before that. The new refrigerant used in most systems is R-134a, which is what the newer stuff should be referred to. I know these are just technicalities, but they can cause confusion at times, especially if you don't say how old your car is. If you say your car has freon, they may think you have an older car, and if you car is an older car it could have either refrigerant in it.