What year is the bike, and what type of shifters would help.
Guessing, as they are Suntour, the are friction downtube shifters; and 7 or less speed, being realistic, there is not much you can change them to, the cost to change to STI's (brifters)would be similar to a new bike; the oply other option would be barend shifter, which again have costs, but less involved with converting to them.
Cost to change is almost prohibitive. Better off keeping an eye out for a replacement, cleaning it really well, selling it, and buying what you want. A Trek 1000 should bring a decent price.
As to your indexing, the old Suntour stuff would index, not flawlessly, but pretty decent. Is your freewheel Suntour, and do the number of cogs match your shifter? And does the RD match the shifters as well? Suntour had various attempts at indexing. I've had several Suntour indexed shifting bikes, and they all shifted OK (but not great).