Yup, basic carrot shape is all about variety - sowing depth is irrelevant. A good all-purpose, moderate and slow-release N fertilizer is Espoma's Plant Tone. It is also organic.

With limited space in my vegetable garden, I started growing potatoes in those large felt bags. They work great for potatoes and, once the potatoes are harvested in midsummer, they work great for carrots, which I then harvest in the fall and winter. I use a nice light potting medium like ProMix in them, so I get beautiful, uniform carrots.

Nantes is another good, plump and stocky carrot. Short and almost cylindrical, it has virtually no tapering or pith/core. And is more tolerant of heavier rocky soils than most other carrot varieties.

afaik, all carrots with other pigmentation (white, yellow, red and purple) will be of normal length and tapering

Danver's Half Long is another good old carrot variety. Agree with the others that the colored carrots I have seen are imperator-types (slim and long).

I don't even fertilize my carrots. Some compost mixed in prior to planting is all they get (same goes for beets and other root crops).

Rodney

Another vote for Nanties, they aren't huge carrots 5-7" but they make up for it in flavor, sweetness, and tender juiciness (sounds like a steak). I find them easier to pick too. We weed them intensely over time and thin to 2" apart in long wide row. Spring planted carrots will get bigger but the sweetest ones are fall grown. Happy Harvest

Concur the Nantes types are the best tasting group, but they are cylindrical carrots with blunt tips

Here's a combo pic of last year's beets and Nantes carrots...

Try Kuroda types, nice sweet thicker carrots. The purple "Dragon" is yellow inside and a really nice carrot, gets somewhat thick. Chantenay are easiest to find in the seed rack, easy to grow.

Shin Kuroda

Purple Dragon

Red Cored Chantenay

Try planting your carrots in late summer so they mature in the fall. After they get frosted they sweeten up and are much better than spring grown for flavor.