I just got an older bike - a Schwinn Paramount Series 7 PGD OS bike. It has 26" wheels.
What is required to convert to disc brakes? Any suggestions on which kit is best to get?
Are there any problems I might have with the conversion?
The photos I have seen on line indicate this bike lacks a frame mount for the rear brake caliper. The fork also lacks a mount. It will be most likely be cost prohibitive to attempt modifying the frame. You would need road specific disc calipers if you will be using drop bars, a disc wheelset, rotors, and cables as the old ones will likely be too short. If you are unhappy with the stopping ability the money would be better spent on quality brake pads.
You're on the slippery slope of knock-on upgrades. Its cheaper to buy a new bike equipped with disks than it is to upgrade an existing bike to discs from rim brakes.
Look for Kool Stop brake pads for your existing rim brakes, which are often salmon-coloured. They work really well, and aren't stupidly-expensive.
Don't buy $2 brake blocks and expect improvements.
Also, discs don't stop any better than rim brakes - so you might want to search this stack for "adjust rim brakes" and see if you can make yours work better.