Illinois Extension said:
Aim to plant root crops by the second week of August for a successful harvest in the fall.
For greatest success, select cultivars with a days to maturity less than 70 days:
Carrots
'Nantes', 'Danvers', or 'Bolero'
These cultivars offer excellent flavor and a crunchy texture, even when stored.
Beets
'Detroit Dark Red', 'Boro', or 'Chioggia'
All are 55-60 days to maturity; all have excellent storage potential and fresh green quality; all have high levels of sweetness.
Turnips
'Purple Top White Globe', 'Tokyo Cross' or 'Hakurei'
Store short term in the fridge, grow 'Purple Top White Globe' and 'Tokyo Cross' for the root.