If it's just for short delays for thickening and general aural effects, any cheapo analogue delay will do. I have an old PSK analogue delay made of finest plastic, which is a pretty good copy of the old Boss analogue delay, and it sounds excellent. I think I bought it for $40 new.
I think the MXR Carbon Copy is over-rated, and
here's why. For the type of thing you're talking about the MXR will do the job, but it's more expensive than some other devices that will do it better.
I would recommend you go to a shop and try some, and don't discount the nasty cheap shite. Danelectro analogue delays, for example. You never know what your ears may turn up if you don't let the sales people bug you too much.