Good pics, they are very useful. first and foremost, are you riding it with the seat in that position? if so, that frame is most likely WAY to small for you. A 5 inch saddle to handle bar drop would be considered a lot on a road bike. your saddle to bar drop isn't that far there but that stem is angled really steeply upwards and you have riser handlebars. but lets say in theory that it is the right size, some issues you need to consider to create a road bike out of this.
1. Brakes- that bike has cantilever brakes, you may have some compatibility issues with the cable pull if you use sti levers for braking. I'm not 100% positive on that but research it further. if you removed the front reflector you could probably mount regular dual pivot caliper road brakes there and a cheap set of those can be found online for around $25 for the pair.
2. Handlebars- You have a threaded headset there so swapping a different stem is more difficult, that stem that is in there now has a ton of rise but that may suit your needs. the real issue is checking the clamp size. most modern drop bars have a 31.8 diameter clamp while most older threaded stems use a 25.4. There are drop bars that are 25.4 in diameter though. in fact, I have a pair of them that also have cross brakes on the tops of the bar that I would sell for cheap. pm me if your interested.
3. Wheels - You want to find out if those are 700c or 27" wheels. 700c is more or less the modern standard but tires are still available for 27" bikes. keep in mind that if you decide to go 8,9, or 10 speed it will require a new rear wheel anyways.
Here is my .02 cents. I would NOT convert that style of bike into a road bike. That bike would make an EXCELLENT commuter/utility bike. the larger tires would make for a comfortable ride on potholed streets and that bike can easily go from pavement to dirt trails without any issues. It appears to be in really good shape and would probably benefit from a few things that an lbs could do rather inexpensively such as checking out the hub bearing, headset bearings and bottom bracket bearings and replacing bearings and grease as needed. If you really want something more modern shifting wise, I would keep it as a flat bar bike and add the microshift flat bar shifters which only cost 30 bucks and the microshift rear deraileur which is also about $30 and would give you indexed shifting. I would then get an inexpensive rear wheel and with a 9 speed casette and call it a day. replace the brake cables if needed but thats it. A decent rear wheel can be had for $50 and a new casette and chain would run you $40. I think your rear deraileur says shimano sis, so you may not even need a new rear deraileur, you may be able to get that one to index.
As is my scenario would still have you spending close to $200 but I think keeping it as a hybrid utility means if its not quite the right size it's less of an issue. If your gonna get a road bike and start doing serious rides of any great length, you really want it to fit pretty decently.