That pump will work reasonably well if you have good air pressure available. Those things eat a lot of air, and don't really pull 30 inches of vacuum like they claim, but will pull a decent vacuum and will help get the correct refrigerant charge into the system. Let it run for 20 minutes or so to get it good and dry. A warm engine will also help push out the moisture.

With the gauges connected, close the valve to the pump and see if the system will hold vacuum. If it holds vacuum, it'll probably hold pressure. If not, hunt down the leaks before you charge it.

Keep track of the oil level. The compressor probably came with oil in it, but each component you replace has a corresponding amount of oil that should also be replaced. The receiver-drier requires an ounce of oil. The proper method is to drain the oil out of the old compressor and make sure that the new one has the same amount of oil in it. If you didn't do that, and the new compressor came with oil in it, you are probably ok to just let it go at that. Maximum total oil in the system should be 5 oz. If you are reasonably close to that (probably 4-6 oz.) you'll be fine.

You don't replace those little springs. They are built into the lines and form the "quick connect" device that allows them to roll these cars down the assemly line at a steady pace. If you used a proper tool to separate the lines the springs should not be damaged.

 

I'd listen to what inverted said and get it done professionally. The system must be kept under a vacuum for at the very least one hour, but most mfg.'s recommend two hours. The vacuum needs to be kept at a certain level too and checked during that time to see if the system has any leaks. If the vacuum changes then the system has a leak which then must be located and repaired before charging the system again. Good luck finding the leak when the system is empty. The pro's have the tools to find the leak. Having it done professionally will insure that your system won't leak and will perform as intended. Buying the equipment will cost you more than having it done and probably a lot more to get good equipment. You should be able to find somewhere that will do it for around $200, maybe less.