Thomas15 I believe you are mistaken that riser bars on an old road bike will not necessarily make for an upright position.. Road bikes and other bikes designed for drop bars are almost universally equipped with a shorter top tube than a comparable muntain bike or other bike designed around flat bars. My experience has been that drop-flat/riser bar conversions almost always result in a very upright position. IF the bike fit the rider well with drops, it will be almost too upright with risers.
For brake levers, you need any lever compatible with road or cantilever (mountain) brakes. Most modern levers for flat bars are intended to be used with long-pull V brakes or disc brakes. Using long-pull levers with the brakes that came on your old road bike will give you very weak brakes that require lots of effort to actuate.
Any friction shifter will work.
mack_turtle says try to find an indexed shifter with the correct number of speeds, but I don't think this will work well - your rear derailleur would need to be designed for use in an indexed system, and this is not likely the case on your 1985 bike.