A rocker and a bouncer are the same thing. Are your parents referring to the old-fashioned mesh bouncers? You can't get them anymore anyway and a second hand one won't meet the Australian standards if that helps!

I used a rocker for both of my boys and found it wonderful. You can take your bub everywhere with you around the house. It's also great for a change of 'scenery' when they get a bit bored on the floor. I think vibrating musical ones are a bit over-rated! Features I like - a sunhood if you think you'll use it outdoors, a toy bar that can be moved out of the way (babies get overstimulated with too many toys so it's handy if you can leave bub in the rocker, but move the toys away when they crack it!) and height adjustable.

I also have a swing which was fantastic when my DS was tiny, but now he is bigger (6 months) he doesn't want to stay in it unless I'm sitting next to him, otherwise he tries to get out of it. So if you get a swing you will probably think it's great, but it's not as versatile as a rocker.

Hope that kind of answers your questions!