I personally don't have any problem with friction shifting, so I'd be inclined to leave the setup as it is, or possibly replace the FD if the mis-match bothers you. But some others no doubt will differ. As others suggested, the decision you'll have to make is whether to D-I-Y or turn it over to a good shop. Working on bikes of this era is pretty straightforward, and your parts are good enough that it's pretty satisfying when you get things adjusted properly. However, it does take time, the right tools, and know-how. If you want to work on the bike yourself, it would be best if you could find someone in your area (through a bike club, the forums, whatever) who could work with you. There are also lots of good resources online. Check the Mechanics forum for specific questions, and refer to the Park Tool website. There are also lots of good tech. tips on Sheldon Brown's (RIP) website.
By the way, your front brake pad holders are on backwards. The pads should slide in from back to front, so that the braking action can't push the pad out of the brake.