As WTD put, you CAN run a DCC fitted loco on a dc track, but the various sounds and functions won't work.
You can NOT put a dc loco on a DCC track, the motor will fry in seconds.
The 'standard' controller you mention is a feeble thing that will not run older loco's for very long, before it overheat and turns itself off until it cools down again.
The power clip/track - the dc one has a capacitor in it, put there to help reduce tv interference, which is not really relevent these days anyway! For a DCC track, this needs to be removed, as it interferes with the digital info sent by the controller, causing all sorts of weird things to happen.
Older loco's may not run very well on modern track. The wheels had larger flanges, which will cause problems on points and crossings, if you have any. Trucks and coaches are 'usually' fairly easy to re-wheel, it depends if they are 'through-the-hole' or pin-point axles,but loco's can be difficult, needing some knowledge, and setting up again. 'New' trains will run on older track.
As said - old track was usually steel (looks grey in colour, and magnets stick to it), but it can rust, and once it has rusted, you are wasting your time trying to 'rescue' it. Nickel-silver track won't rust, magnets won't stick, and it looks shiny.
Some people have TWO layouts, one with older track for the older trains, and another with modern track, for the newer items.