I agree that brands don't matter. I ride a Raleigh from the late seventies and a Schwinn from the early nineties. I just look for bikes with frames that I can put new components on. I don't want a bike "restored" to original condition, because then I'm stuck with components that are years out of date.
I'd avoid the bikes with one piece cranks. While they are generally cheaper, they aren't but five or ten bucks cheaper. One piece cranks really limit you on upgrading components. Pedals being one of them. You'll likely be limited to platform pedals. Though a converter can be purchased to allow you to use other cranks, the cost of the converter way outstrips any savings you had by getting the bike for pennies.
I know, I had a bike that I kept for 35 plus years. It rode very nicely. But when I decided to move to clipless pedals because I was riding at higher cadences, I couldn't. So off to craisglist it went and I got my Raleigh for very cheap in nice condition. A crankset and freewheel upgrade from 5 to 7 speeds made it a good deal for me.
Staying with english threaded bottom brackets 1.375" diameter and 24 tpi. will make it easy to still find modern components from just about any manufacturer like Shimano, Campy, FSA, RaceFace, etc.
But if you already have a bike that rides nice. Ride if for a year and get yourself aquainted. Find out what it does you like and what you don't like. Find out if you are going to be riding at a leisurely pace for a low cardio workout or are you going to be riding to push your cardio to it's max.