I've built several red systems and this is what I would recommend:
1. Go on youtube and enter "SMD soldering". There are several good videos and the SMDs cause the most problems.
2. Clean the boards both sides before starting. IPA can be used, I use something called "switch contact cleaner". Make sure it is dry before starting.
3. Separate out all the parts by type and count to make sure the count is right and they are all the same.
4. Mount the SMDs first. I use liquid flux and solder paste for these and use a hot air soldering machine to solder them. If you use regular solder and an iron, I'd cut toothpicks in half and super glue them to the top of the chip so I can hold it in place. Trying to hold them with tweezers or anything else is beyond me. People that can do that must have nerves of steel.
5. WalMart sells "readers" that make great magnifying glasses for about $5. Trying to hold a chip in place, solder it and hold a magnifying glass requires three hands
6. Before doing anything else, clean the joints with IPA to get rid of the flux, wipe down well with a wipe and inspect the joints. Of the boards I've repaired 90% are because of those solder joints. At this point, repair is pretty easy. Once the other parts are in place getting a soldering iron in there is a bitch. I have a 20X jewelers loupe that I inspect with.
7. There's a chart in the manual of the parts and the quantity. I lay all the parts out just like the chart and work my way down.
8. I check all the resistors with a multimeter and make sure they are the right value and separate them by value.
9. I start with the smallest parts in size and work up to the largest.
10. I use standard 60/40 electronic solder
11. When I get everything assembled, I use my hot air system from the back side and slowly go over the whole board. It is effectively reflowing the whole thing.
12. As a final step, I spray the board with IPA until it is good and wet and wipe it dry to remove any flux residue.
If you have to remove an SMD, hot air is the only way to go. Many places that work on computers have one and will let you use it. I've tried everything in the world and nothing else works without some damage to either the SMD or the board.
The SMDs used are really durable. I've seen them put in backwards, off a pin and burnt to a crisp and still work.
I work with the board on a white towel. It helps to hold the board in place and see dropped parts.
I've done trouble shooting on several red systems and 90% were SMD problems. Bad solder joints, bad location or in backwards. If you can get the SMDs in good, the rest is simple.