Are running shoes or walking shoes or cross track trian shoes best for cardiovascular exercise?

This depends somewhat on what your fitness level and what you are actually doing?

If you are pretty out of shape and so when running or cross training etc will be doing relatively "light" exercise the shoes are not that important.

However if you are mostly running (whatever your fitness level) you would be better off going for running shoes anyway. They will give you the right support for running and will be fine for most other cardiovascular activities too (even if not optimal).

Running shoes are for jogging, walking and running generally without a lot of sudden sideways movement.
X training shoes are for activities that require a lot of sideways movent and stop stary movements like Aerobics and other fitness classes , Netball and other similar sports when you dont wear cleats or specialty shoes.

You are usually best getting shoes fitted at a specialty store that can match the right shoe to your normal foot movement (pronation etc.) and activity.

In general, running shoes give you the most support, whatever you are doing.