If you haven’t soldered electronics before, then it may be more prudent to have a local repair shop do it. $100 is standard for this type of job. Typically, they will charge a minimum of 1 hour labor. Like steakster said, it can cost some money to buy good enough soldering iron and actual electronics solder. You might be close enough to the $100 already. The cheaper 25-40 watt soldering irons you can buy at home depot can work, but you may be there for a while heating up solder. This can require a long enough time where you might actually damage some element (like an IC or capacitor, etc.). Some solder points on electronics equipment and PCB can be stubborn, even for my 70 watt Hakko.
As for solder, Home Depot will probably not have the correct stuff. DO NOT buy acid core solder for electronics. For rosin core solder, you’ll want to get as thin solder as possible. Home Depot may have this, but mostly it is the thicker solder that is harder to work with on electronics. Also, for this quality of amp, you’ll probably want to get the better silver/copper type solder. You can get a small roll of Cardas solder from Parts Connexion for $25.
If you are intending to get into doing DIY stuff, then great. Soldering a new RCA input can be an easy job (depending on if you have to deal with PCB mount RCA connector or if they are just wired). Otherwise, it might be better just to have a repair shop do it.