I've never used anything except friction shifters. The few times I've fooled around with indexed shifters in shops, it felt very unnatural; I don't know if I could ever get used to them.
When considering a used bike, here are some of the things I look for: Check the frame for cracks, especially around the joints between tubes, and around the bottom bracket. If it's a brazed steel frame, look along the edges of the brazing lugs for gaps that might indicate the brazing has been damaged. Look also for any bends or dents, and for places where the paint looks stretched or bubbled up, because that could indicate damage below the paint. From the side of the bike, push and pull the cranks back and forth to be sure there's no sideways movement that could mean worn bearings. Do the same with the wheels to be sure the hubs are tight, and check for any looseness of the fork in the head tube. Look for frayed or rusted brake and shifter cables, and kinks or cracks in the cable housings; see that the brake levers move smoothly and that the brake pads meet on opposite sides of the wheel at the same time. Also see if the brake pads are wearing evenly. Spin the wheels and watch them where they pass between the brake pads; look for wobbling side-to-side or up-and-down. Operate the shifters and watch the derailleurs; they should remain parallel to the chainwheels and gears throughout their full range of motion. The friction shift levers should move smoothly and should stay exactly where you put them, without creeping forward or backward. (You may need to tighten them if they're loose, but work them back and forth to make sure they stay tight.)