Shudra(s) is the fourth Varna in the varnashrama system, they are the only one who cannot be dvijas which means they cannot undergo upanayan samskar and thus cannot read the Veda or hear them.
Thus for their benefit, they shall read various Purana(s) and Itihaas (Ramayan & Mahabharat), as Veda(s) are presented in a simplified form for their benefit.
Shudra(s) are meant to serve the other classes by various means such as by becoming sculptors, artists, dancers, singers, engineers etc.
In Bhagvad Gita (18.44) following has been said about their duty.
Krisi go raksya vanijyam
Vaisya karma svabhavajam
Paricaryatmakam karma m
Sudrasyapi svabhava jam
Translation- Agriculture, protection of the cows and business are prescribed work for the vaishyas, and for the sudras the dharma is labor and service to others (other varnas).
Now the other thing about Shudra(s) is that it is not that they cannot attain Bhagvan or perform his bhakti. It is only that they are not eligible to be Dvijas and thus are excluded from Vedic study.
Same thing is applicable to women as they cannot too become Dvija.
Even though Vidura was Shudra still he was respected by all and served as a minister to Dhritarashtra, the king of Hastinapur (Mahabharat).