I rescued a 88 Trek 1000 for my son early this years what was parked outside long enough for the tires to rot to threads along with the inner tubes, rim strips, and seat. Surprisingly all it need was tires, tubes, rim strips, a chain, seat, and brake cables. I cleaned and lubricated all of the bearings myself, and only had to touch the wheels up (truing).

Your existing bike has the advantage of being a perfect fit for you. Sounds to me like what it needs is the same thing that I did to the Trek for my son, with the addition of needing to replace the shifters. Are you sure they are worn-out? Are they sticking, or just aren't shifting right? If the bike was outside all that time, new shift cables (housings and inners) and adjustment might be all they need to be put back into working order. If you are forced to replace the shifters, your $100 estimate could be eaten by replacement shifters alone. Safer to plan on $150-$200 for parts in case the shifters need replacement.