Gunas are tattvas created from Prakriti/Nature/Maya.:
सत्त्वं रजस्तम इति गुणा: प्रकृतिसम्भवा: |
निबध्नन्ति महाबाहो देहे देहिनमव्ययम् || b.g. 14.5 ||
O mighty-armed Arjun, the material energy consists of three guṇas (modes)—sattva (goodness), rajas (passion), and tamas (ignorance). These modes bind the eternal soul to the perishable body.
न हि कश्चित्क्षणमपि जातु तिष्ठत्यकर्मकृत् | कार्यते ह्यवश: कर्म सर्व: प्रकृतिजैर्गुणै: || b.g. 3.5 ||
There is no one who can remain without action even for a moment. Indeed, all beings are compelled to act by their qualities born of material (motherly) nature (the three guṇas).
Bhagawan Shiva is above Prakriti.:
“maayaa.n tu prakR^iti.n vidyaanmaayina.n cha maheshvaram.h |
tasyavayavabhuutaistu vyaapta.n sarvamida.n jagat.h |” (Swetasvatara Upanishad 4:10).
“Know then Prakriti (nature) is Mâyâ , and the Maheshwara the Mâyin; the whole world is filled with what are his members (forms)”.
"kṣaraṃ pradhānam amṛtākṣaraṃ haraḥ kṣarātmānāv īśate deva ekaḥ |
tasyābhidhyānād yojanāt tattvabhāvād bhūyaś cānte viśvamāyānivṛttiḥ ||" (Swetasvatara Upanishad 1:10)
"Prakriti (Pradhana) is perishable. Hara, the Lord, is immortal and imperishable. The non-dual Supreme Self rules both prakriti and the individual soul. Through constant meditation on Him, by union with Him, by the knowledge of identity with Him, one attains, in the end, cessation of the illusion of phenomena."
Bhagawan Shiva as Sattvik and Pusuhottoma.:
प्रथमा रक्तपीता महद्ब्रह्म दैवत्या ।
द्वितीया विद्युमती कृष्णा विष्णुदैवत्या ।
तृतीया शुभाशुभा शुक्ला रुद्रदैवत्या ।
यावासानेऽस्य चतुर्थ्यर्धमात्रा सा विद्युमती सर्ववर्णा पुरुषदैवत्या ।
The first is the red Lord Brahma ( creative aspect ) , the second the black Lord Vishnu ( the administrative aspect ), the third the holy white Lord Rudra ( destructive aspect ) , and the fourth which is like lightning is the multi-coloured (have all aspects) Purushothama (Shiva). (AtharvaShikha Upanishad 1.7).
Maitreya Upanishad also confirms this.:
सर्वदा समरूपोऽस्मि शान्तोऽस्मि पुरुषोत्तमः ।
III-24. "I (Shiva) am always equanimous, I (Shiva) am quiescence, the greatest being (Purushottama);"
And Also,
Rig-Veda Khilla Part, Shiva Sankalpa Shuktam.:
यो वै वेद महादेवं परमं पुरुषोत्तमम् ।
यः सर्व यस्य चित्सर्व तन्मे मनः शिवसंकल्पमस्तु ।। 21
21. The one who knows the great God (Maha Deva), Om the highest of Persons (Param Purushottoma) of the vedas, Om the Supreme Self, may such my mind be of beautiful and divine resolves, be always remain filled with Auspicious Shiva-thoughts.
Bhagawan Shiva as Ardhanareshwara (Krishna-Pinglam) as all 3 gunas and rules with Mula-Prakriti (Uma).:
“athaasya yaa sahajaastyavidyaa muulaprakR^itirmaayaa lohitashuklakR^ishhNaa |
tayaa sahaayavaan devaH kR^ishhNapi~Ngalo mameshvara iishhTe |” (Shandilya Upanishad 3:01).
“Maheshvara (the Great Lord Shiva) who is black and yellow (Krishna-Pinglam/Neela-Lohita) rules with Avidya, Mula-Prakriti (Uma) or Maya that is red (Rajas/Mahalakshmi), white (Sattva/Mahasaraswati) and black (Tamas/Mahakali) and that is co-existent with him”.
Bhagawan Shiva is also Nirguna.:
योऽसौ सर्वेषु वेदेषु पठते ह्यज ईश्वरः । अकायो निर्गुणोऽध्यात्मा तन्मे मनः शिवसंकल्पमस्तु ।। 18.
18. The one that is recited soundless in all the Vedas, non-pierceable incorpeal self (atman), may such my mind be of beautiful and divine resolves, filled with Auspicious Shiva-thoughts. (Shiva Sankalpa Shuktam Rig Veda Khila).
Bhagawan Shiva as the Lord of the Sātvik People.:
“dhavathe sathvanaam pathaye namo namah |” (Yajurveda Sri Rudram Anuvaka -2).
“Salutations and salutations, to him (Rudra), the all pervading one, who rushes to save his devotees, And to him who is the lord of people with Satva qualities”.
Even Smritis like Itihasa, Purana, Upa-Purana, Geeta, etc says the same.:
Mahabharata Anushasana Parva.:
tapaś ca sattvaṃ ca rajas; tamaś ca tvām eva satyaṃ ca vadanti santaḥ". (MBH 13:15:30).
The blessed Vishnu (Krishna) said, 'I saluted Mahadeva, saying,--Salutations to thee, O thou that art the eternal origin of all things. The Rishis say that thou art the Lord of the Vedas. The righteous say that thou art Penance, thou art Sattwa, thou art Rajas, thou art Tamas, and thou art Truth.
Sri Shiva Purana 2.1:1:16.:
36. Śiva manifested himself in three ways in the form of Vaikuṇṭha (Viṣṇu) born of the left limb, in my form (of Brahmā) born of the right limb and in the form of Rudra born of the heart.
37. Viṣṇu, Rudra and I (Brahma) represent the three Guṇas. Śiva is free from Guṇas. He is the supreme Brahman, the undecaying.
38. Viṣṇu is of Sattva attribute, I (Brahmā) am of Rajas attribute and Rudra is of Tamas attribute. This is only in view of the activities in the world. But in fact and in name it is otherwise.
39. Viṣṇu is of Tāmasika nature within but externally Sāttvika; Rudra is of Sāttvika nature within but of Tāmasic nature outside, I am of Rājasic nature throughout.
40. The goddess of speech is of Rājasic nature; Satī is of the Sāttvika nature and Lakṣmī is of Tamasic nature; The great goddess Śivā is of the three natures.
Here's one more from Soot Gita.:
Soot Gita (2.40-41).: asti rudrasya viprendrA antaH sattvaM bahistamaH | viShNorantastamaH sattvaM bahirasti || rajoguNaH antarbahishcha viprendrA asti tasya prajApateH |
Rudra the Lord of the Brahmanas is of Sattvika nature from internally and Tamasik nature from externally.
Vishnu is of Tamasik nature from internally and Sattvik nature from externally.
Prajapati (Brahmā) is of Rajasik nature from both internally and externally.
There is another confirmation in Shiva Dharmottara Purana.:
Shiv Dharmottar Purana.: antah sattvagunopeto bahistaamasasamyutah shuddha saattvika ityuktah shankaro lokashankarah । antastaamasa shamyuktto bahih sattvagunaanvitah shuddha taamasa ityukto vishnussaakshaat sriyah patih ।।
Lord Shankara is endowed with Sattva guna internally and Tamasik guna externally. So, the Lord of the World (Shankara) is purely Sattvik in nature.
Lord Vishnu is endowed with Tamasik guna internally and Sattvik guna externally. So, The Husband of the Sri (Vishnu) is purely Tamasik in nature.
As for the classification of the Purānas, you can see this answer of mine.
I hope this clarifies all your queries. Prd..
