What I don't know is what stem to use to convert it. I've never worked on a bike this old. My experience is mostly with recent road bikes = threadless 1 1/8. This one looks to be a 1 inch headset / stem.
Get a digital caliper, but my guess is that you have one of those .833 stems, found on bottom end bike, BMX bikes and some Schwinns. I hope I am wrong. In that case, the cheapest option is to find a suitable flat bar donor bike. I picked up a Huffy ten speed just for that purpose. Cost me $2.75 at a church sale. Stem, bars, grips and levers are going onto an older mixte I have that also has a .833 stem.
I'd be very hesitant to put any money into a bike that low-end. Do you really need a different stem? I'd just raise it to its max mark, install a cheap steel bar with cheap Tektro levers and cheap rubber grips, and leave it at that. Use a cheap riser bar if you want more height.