Others have given some great advice. I mainly just want to say welcome, and it will be fun to watch your progress. You are starting with a very ambitious plan here, but you are the best judge of how much time and dedication you can put into this hobby. It will be good to try some practice techniques with the big quantity of airplane fabric first.
If you pre-wash, you'll need to either pink or overcast the raw edges of the fabric before you wash to avoid a huge tangled mess of threads and possible distortion of the fabrics. You don't need a serger to do overcasting. If you have never done it before, check your machine's manual to see if you have an overcast stitch and foot. If not, your widest zigzag will do. They sell pinking blades for rotary cutters if you don't already have pinking shears. You'll probably want an extra cutter for this purpose because switching the blades frequently is a pain.
Use Color Catchers (a product sold in grocery store laundry aisles) to help keep the colors from running amok. Bleeding dyes are not common, but can be such a headache when you encounter them. You're off to a great start in picking fabrics with good contrast. Use color catchers again after you finish the quilt. I like to use washable glue sticks to baste my binding, and therefore always wash my quilts before giving them to anyone.
I usually start by making sure I have enough fabric for the project before I cut anything because otherwise you may come up short after doing quite a lot of work. However, if you only have enough for a small middle area, you can always make a quilt bigger by adding wide borders. A design wall is very useful for laying out your blocks and making sure everything is in the right order before you start joining them. It can be as simple as a piece of batting tacked to the wall, but if the air conditioner is blowing toward the pieces they may fall off and need to be pinned in place. It's easy enough to lay out a smaller design on a bed, but not if you have pets or kids who like to rearrange things for you, and not if you or somebody else is planning to sleep in that bed every night.
If you are planning to do the quilting on your Singer, be aware that the bigger the quilt the more of a challenge that will be. Try it on something small before you set yourself up for disappointment. I'm not saying it's not possible, but it certainly can be difficult. Marti Michell has a book about quilting in sections that might be helpful. (Maybe no longer in print, but possibly in your library or on a used book site.) If you can place an additional table to the left of where you sit at your machine to help support the weight of the quilt, that's a good idea. Start near the center and work outward. You don't want to have more than half of a big quilt in the area to the right of the needle.
There are different ideas about how binding should be done. You will want to compare and decide whether you intend to use the machine to finish it or do the final round by hand. I usually do mine by machine, but it's still a challenge after a lot of years. It's actually easier to get it right by hand-sewing the final round, but that takes several hours.
Google for a quilt guild in your area. They can be a wonderful resource, and it's encouraging to know others who have been there, done that. Quilt shops and sewing machine stores also sometimes have quilting groups that meet regularly and also they may offer lessons.
Best wishes!