Carrots are an ideal container crop plant into a deep container with plenty of growing room. It is also important to replicate the best growing conditions, which means fine, free draining soil with no lumps and which runs freely, sieved is best. Also essential will be to protect the carrots in the container from carrot fly with mesh.
Helpfully, in 2010 the RHS undertook a trial to establish which varieties of Carrot are most suitable for containers and best early varieties and the results of their trial are: Marion F, Parmex (a very short variety,) Adelaide F which described as sweet flavoured, Parano, Nantes 1087 F, Mokum F, Napoli F, Primo F, Trevour F, and Yukon.
Carrots which have the RHS award of Garden Merit are: 'Resistafly' a Nantes type with some resistance to carrot fly; 'Eskimo' all rounder that is winter hardy, particularly in well-drained conditions; 'Deep Purple' unusual colour; 'Artemis' smooth skinned good as baby carrot.
There are also seeds sold which produce a mixed range of colours for Carrots sold as 'Rainbow' Mix which as the image shows produces multi coloured carrots. Most of the garden centres and on-line web retailers have a wide range of carrots including the multi coloured variety. Originally carrots were purple and white, the orange carrot only made its appearance in the 1700.
There are 7 main types of carrots:
Nantes which can be earlies or main crop and form a cylindrical carrot. They are widely grown commercially.
Amsterdam forcing are a mainly slender carrot with cylindrical roots
Chantenay has conical roots and is good for shallow soil and containers, Berlium similar but smaller.
Autumn King large carrot but maybe not as tasty
Globe has shallow roots and good for growing in containers and grow bags
Imperator mainly grown in US.