Salaam Alaikum,
Firstly like the other brothers pointed out Salafi’s do not reject Ahadith but believe in and follow the Sunnah of the Prophet (peace and blessings be upon him). Salafi’s believe that the Messenger (peace and blessings be upon him) never spoke anything from himself rather it was inspired to him by his Lord Allah (the Exalted and Majestic) and we believe that no body can practice Islam with Quranic knowledge alone. In fact the other name for Salafi’s is Ahl-ul-Hadith or back home in Pakistan and India its Ahl-e-Hadees.
Secondly like the other Muslims Salafi’s believe that a persons faith can never ever be complete until that person loves Muhammad Mustafa (peace and blessings be upon him) more than his own self, his children, his parents, his siblings and all of creation but we love no one like we love Allah (the exalted and majestic) and worship only Him, pray to only Him and ask for help (from the unseen) only from Him.
And as for following one of the four Imams well… The Salafis respect all four of the Imams and acknowledge their hard work but the four Imams were only human beings and made mistakes. Sometimes they only had access to weak or fabricated Ahadith and sometimes a Hadith did not reach them because the books of Ahadith e.g. Bukhari and Muslim were compiled after the four Schools of thought began.
All four Imams would tell their students and other people to ignore their rulings if they go against Ahadith of the holy Prophet (peace and blessings be upon him).
*“This is my opinion, but if there comes someone whose opinion is better than mine, then accept that.” [Imam Abu Hanfia]
“I am only human, I may be right or I may be wrong, so measure my words by the Quran and Sunnah.” [Imam Maalik]
“If the hadith is authentic, then ignore my words. If you see well established evidence, then this is my view.” [Imam Al-Shaafa’i]
“Do not follow me blindly, and do not follow Maalik or al-Shaafa’i or al-Thawri blindly. Learn as we have learned.” [Imam Ahmad Ibn Hanbal]*
Salafis follow these Imams when their rulings and opinions are backed by evidence from the Book of Allah or authentic Ahadith and if that is not the case then they look towards the opinions of other trust worthy scholars both past and present. No one should follow any one Imam stubbornly and blindly rather he should accept that which is in accordance with the truth weather it is from his Imam or anyone else.
It is better for a person who has knowledge of the Quran and Sunnah to derive rulings themselves.
Allah (the Exalted) knows best.
May Allah bless our Prophet Muhammad (peace be upon him), his family and his companions.
Wassalaam.