Front end problems

Check the easy stuff first. What color is the brake fluid in the master cylinder? If it's anything other than clear, it needs to be flushed out. You say the brake pads are new, what do the brake hoses look like? New? Or old and rotted looking? Is this a car with power brakes or manual?

With a "new to you" car, it's always best to start with the easy stuff. Brake fluid and hoses are cheap. If the problem persists after that, move to master cylinder and then the calipers. If it's a power brake car look at the booster too. The hoses go bad MUCH more frequently than the calipers do. In fact, in my experience anyway, the master cylinders fail more often than the calipers do. I have the stock and apparently original calipers on several of my cars. I have the original brake hoses and master cylinders on exactly none of them. The single piston 73+ calipers are pretty reliable, they're not nearly as prone to issues as the earlier Kelsey Hayes calipers. I've even used 73+ calipers straight out of the local wrecking yards, unknown history, unknown miles, crusty looking, the whole bit. Pistons moved freely in all of them. And if the brakes seem to work ok and then get worse as you drive, the calipers wouldn't be my first suspect.