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 make cylindrical carrots and are widely grown commercially.
Amsterdam forcing more variable and mainly slender cylindrical roots
Chantenay conical roots and good for shallow soil and containers
Berlium similar but smaller
Autumn King large carrot but maybe not as tasty
Globe shall roots good for containers and grow bags
Imperator mainly grown in US.
If your growing conditions are not ideal more success can be obtained from growing a F1 hybrid, such as Primo and selecting carrots seed such as Primo which the RHS such as flyaway, deep purple Nepal, Extreamo (maincrop) Amsterdam forcing 3 - the packets will bear the logo.