Which Carrots?

We have a heavy clay soil and tried short rooted varieties first with laughable results(plant March/April crop mini baby carrots at Christmas..),however since we have started digging sand as well as compost into the beds(builders and now sandpit sand)our carrots have been fab.and some accidentally grown in barrels are still cropping now.
Slug protection is a must or you will get all excited about emerging carrots and 2 days later they could be razed to the ground.Carrot fly is a pest but apparently can`t fly very high so mesh can be used or little mesh/plastic barriers around carrot beds and this is also why you hear about peeps growing in baths as the height is enough to avoid carrot fly and the soil conditions are in your control...wouldn`t mention this except OH moved a cast iron bath in the garden last year...