Which are considered to be the oldest suttas?

There are several collections of texts in the Khuddaka Nikaya that are very old. The Sutta Nipata and the Itivuttaka have already been mentioned, but possibly the Udana is very old as well. Also some of the short fragmentary material in the Samyutta Nikaya and the Anguttara Nikaya are hypothesized to be from the oldest stratum of the Canon.

According to Pande, T.W. Rhys Davids places the chronology of the nikayas midway between the parnibbana and Ashoka, which accepting the modern date for the parinibbana of circa 400 BCE would place the composition of the nikayas about 325 BCE, merely 75 years after the death of the Buddha, but after the Parayana Vagga, Octades (Atthakka Vagga), and Patimokkha. The Atthakavadda and Parayanavagga may be found in the Khuddaka Pitaka, as the fourth and fifth sections of the Suttanipata. The pattimokkha is of course a summation of the Vinaya. Thus, these appear to be the oldest parts of the Pali Canon. (G.C. Pande, Studies in the Origins of Buddhism, 5th ed., Delhi: Motilal Banarsidass 2006, p. 20.)

Gombrich suggests that the nikayas are mid-4th century BCE. Rupert Gethin criticizes this view and suggests that they are somewhat later, "a few generations" after the parinibbana. ("Gethin on Gombrich: What the Buddha Thought")

According to noted University of Toronto Buddhologist A.K. Warder "the order of the five 'traditions' [referring to the agamas, a.k.a. nikayas] happens also to be the order of their authenticity." The first of these is the Digha Nikaya (Skt. Dirgha Agama). Warder claims that this is proved by "comparing the various available recensions." B.C. Law divides the Digha in half, placing the first part earlier than the second and third parts, which postdate the Four Great Nikayas, and distinguishes between an earlier pattimokkha of 152 rules and a later pattimokkha of 227 rules. Warder also considers the Ksudraka or Minor Tradition to be the least authentic portion of the Canon. At the same time he recognizes the Khadgavisanaghata, Munigatha, Sailagatha, Arthavargiyani Sutrani, Parayana, Sthaviragatha, Sthavirigatha, and Ityukta to constitute the "original nucleus of the Ksudraka common to all the schools," whereas the Udanas, Jatakas, and Avadanas "seem at least in origin to have been nothing but anthologies from the Tripitaka." (Warder, Indian Buddhism, 3rd rev. ed., Delhi: Motilal Banarsidass, 2000, pp. 196ff.).

I was told that the Sutta Nipata is a one of the oldest collections. I'm no Buddhist scholar so I can't help with any great textual analysis of the sutta. However Thanissaro Bhikkhu says here that the The Parayana Vagga is quoted in other (more recent) parts of the Pali Canon so this makes it a good candidate to be considered one of the oldest. To quote the relevant part of the passage

There is evidence that these sixteen dialogues were highly regarded right from the very early centuries of the Buddhist tradition. [...] Most of the Cula Niddesa, a late addition to the Pali canon, is devoted to explaining them in detail. Five discourses — one in the Samyutta Nikaya, four in the Anguttara — discuss specific verses in the set

The first Sutta preached by Lord Buddha was Dhamma Chakka Pawaththana Sutta, the sutta which is about the Four Noble Truths. You can read it in detail here. The sutta was preached to the Five Ascetics. Konadanna Ascetic could become Sotapanna after listening to the Sutta. Other four Ascetics became Sotapanna after Lord Buddha guided each ascetic with "Kamatahan". And the second Sutta preached was Anantha Lakkhana sutta which was about Not-Self. The second Sutta was also preached for the Five Ascetics(Or now the Five Sotapanna) who became Arahat after listening to the sutta. Adittapariyaya Sutta is also one of the oldest suttas which was preached for 1000 monks.